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Millimeter-Wave and Terahertz
Imaging Techniques
Author
Enrique Nova Lavado
Thesis Advisor
Jordi Romeu Robert
AntennaLab
Universitat Politècnica de Catalunya
Departament de Teoria del Senyal i Comunicacions
Submitted to the Universitat Politècnica de Catalunya (UPC) in partial
fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
April 26, 2013
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Thesis written by Enrique Nova.
Millimeter-Wave and Terahertz Imaging Techniques
Ph. D. program on Signal Theory and Communications
The work presented in this thesis has been supported in part
by the Spanish Interministerial Commission on Science and
Technology (CICYT) under projects TEC2010-20841-C0402, TEC2011-25865 and TEC2011-28201-C02-01, CONSOLIDER CSD2008-00068 and by the “Ministerio de Educación y Ciencia” through the FPU fellowship program.
c
Copyright 2012,
Enrique Nova. All rights reserved.
Reproduction by any means or translation of any part of this
work is forbidden without written permission of the copyright
holder. Requests for permission or further information should
be addressed to [email protected]
Dedicatoria
Abstract
This thesis presents the development and assessment of imaging techniques in the millimeterwave (mmW) and terahertz frequency bands. In the first part of the thesis, the development of
a 94 GHz passive screener based on a total-power radiometer (TPR) with mechanical beamscanning is presented. Several images have been acquired with the TPR screener demonstrator, either in indoor and outdoor environments, serving as a testbed to acquire the know-how
required to perform the research presented in the following parts of the thesis.
In the second part of the thesis, a theoretical research on the performance of near-field
passive screeners is described. This part stands out the tradeoff between spatial and radiometric resolutions taking into account the image distortion produced by placing the scenario in
the near-field range of the radiometer array. In addition, the impact of the decorrelation effect
in the image has been also studied simulating the reconstruction technique of a synthetic aperture radiometer. Guidelines to choose the proper radiometer depending on the application, the
scenario, the acquisition speed and the tolerated image distortion are given in this part.
In the third part of the thesis, the development of a correlation technique with optical
processing applicable to millimeter-wave interferometric radiometers is described. The technique is capable of correlating wide-bandwidth signals in the optical domain with no loss of
radiometric sensitivity. The theoretical development of the method as well as measurements
validating the suitability to correlate radiometric signals are presented in this part.
In the final part of the thesis, the frequency band of the imaging problem is increased to
frequencies beyond 100 GHz, covering the THz band. In this case the research is centered in
tomographic techniques that include spectral information of the samples in the reconstructed
images. The tomographic algorithm can provide detection and identification of chemical
compounds that present a certain spectral footprint in the THz frequency band.
Keywords:Aperture Synthesis, Optical Modulation, Passive Interferometry, W-band Radiometry, Near-Field Imaging, Radiometric Sensitivity, Passive Screeners, Terahertz Tomography, Terahertz Spectroscopy, Diffraction Tomography.
Contents
1
Introduction
1.1 TeraSense project . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Millimeter-wave technology and applications . . . . . . .
1.2.2 Millimeter-wave passive imaging for personnel screening .
1.2.3 Terahertz systems and applications . . . . . . . . . . . . .
1.2.4 Terahertz spectroscopy and tomography . . . . . . . . . .
1.3 Objectives and scope of the thesis . . . . . . . . . . . . . . . . .
1.3.1 Objectives appearing in this document . . . . . . . . . . .
1.3.2 Objectives excluded from this document . . . . . . . . . .
1.4 Organization of the document . . . . . . . . . . . . . . . . . . . .
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Close-Range Millimeter-Wave Passive Systems
2
Millimeter-wave radiometric imaging
2.1 Millimeter-wave radiometry . . . . . . . . . . . . . . .
2.1.1 Thermal radiation and Plank’s law . . . . . . . .
2.1.2 Antenna surrounded by a black body . . . . . . .
2.1.3 Gray body radiation and apparent temperature . .
2.1.4 Image temperature contrast . . . . . . . . . . . .
2.2 Total-power radiometer with mechanical beam-scanning
2.2.1 Total-power radiometer system design . . . . . .
2.2.2 Calibration . . . . . . . . . . . . . . . . . . . .
2.2.3 Performance Assessment . . . . . . . . . . . . .
2.2.4 Description of the antenna system . . . . . . . .
2.2.5 Beam distortion . . . . . . . . . . . . . . . . . .
2.2.6 Imaging Performance . . . . . . . . . . . . . . .
2.3 Synthetic Aperture (SA) Interferometric Radiometry . .
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2.4
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2.3.1 Time-domain correlation . . . . . . . . . .
2.3.2 Visibility function . . . . . . . . . . . . .
2.3.3 Beamwidth of the synthesized beam . . . .
2.3.4 Pixel overlapping in the synthesized images
2.3.5 Radiometric sensitivity . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . .
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Millimeter-wave Performance Constraints
for Passive Close-Range Screening
3.1 Close-range aperture synthesis . . . . . . . . . . . . . . . . . . . .
3.1.1 Single element constraints . . . . . . . . . . . . . . . . . .
3.1.2 Particularized radiometric sensitivity . . . . . . . . . . . . .
3.1.3 2D synthetic aperture interferometric radiometer . . . . . .
3.1.4 1D synthetic aperture interferometric radiometer . . . . . .
3.1.5 Real aperture radiometer . . . . . . . . . . . . . . . . . . .
3.1.6 Far field radiometric sensitivity . . . . . . . . . . . . . . .
3.2 Screener design parameters . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Radiometric sensitivity comparison . . . . . . . . . . . . .
3.2.2 One-Dimensional Synthetic Aperture (1D-SA) sparse array .
3.2.3 1D-SA screener with moving walkway . . . . . . . . . . .
3.3 Screener performance . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Spatial/Radiometric resolution tradeoff . . . . . . . . . . .
3.3.2 Off-axis performance degradation . . . . . . . . . . . . . .
3.3.3 Decorrelation effects . . . . . . . . . . . . . . . . . . . . .
3.3.4 Improved performance . . . . . . . . . . . . . . . . . . . .
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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One-dimensional Synthetic Aperture Radiometer with Optical Signal Processing
4.1 Optical modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 LiNbO3 phase modulators . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Optical phase modulation by a CW signal . . . . . . . . . . . . . . .
4.1.3 Cross-correlation of double-sideband optical modulated signals . . .
4.1.4 Cross-correlation of single-sideband optical modulated signals . . . .
4.1.5 Optical correlation measurements of Radiofrequency (RF) noise . . .
4.2 Millimeter-wave interferometry measurements with optical signal processing
4.2.1 Phase switching technique . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Fringes created by a point source . . . . . . . . . . . . . . . . . . . .
4.2.3 One-dimensional image . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Optical signal distribution for cross-correlation of multiple receivers . . . . .
4.3.1 Distribution technique . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 System Performance Considerations . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Radiometric sensitivity . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Terahertz Imaging
5
Terahertz Tomographic Imaging
5.1 Terahertz diffraction tomography . . .
5.1.1 Reconstruction algorithm . . .
5.2 Imaging scenario simulations . . . . .
5.2.1 Simulation scenario . . . . . .
5.2.2 Spectroscopic imaging . . . .
5.3 Measurements . . . . . . . . . . . . .
5.3.1 Setup and sample preparation
5.3.2 Complex data acquisition . . .
5.3.3 Data calibration . . . . . . . .
5.3.4 Spectroscopic characterization
5.3.5 Tomographic imaging . . . .
5.4 Conclusions . . . . . . . . . . . . . .
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Thesis Conclusions
6
Conclusions and discussion
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6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A Close-Range Millimeter-Wave Passive Images
113
Bibliography
118
Author Publications and Patents
125
Journal articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Conference articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
C HAPTER 1
Introduction
aim of this chapter is to introduce the context, the scope, the objectives and the structure of the research presented in this document. The first section is devoted to describe
the framework in which the thesis has been developed: the TeraSense project. The second
section contextualizes the research performed in this thesis by showing the current state of
the art of the studied topics. The state of the art is followed by enumerating the objectives
and the scope of this thesis. Finally the structure and organization of the work is described.
T
HE
1.1
TeraSense project
The research presented in this thesis is part of an initiative to promote the development of the
Terahertz technologies in Spain with the coordination of the Polytechnic University of Catalonia (UPC). This initiative is concentrated in the TeraSense project where 16 research groups
of 11 Spanish universities work together to improve the knowledge related with Terahertz
systems. The research groups participating in the project are specialized in electrodynamics,
high frequency technology and design, numerical simulation and computer engineering. The
diversity of expertise found in the research groups has been an advantage to face the scientific
challenges that appear in the THz frequency range. The main objectives and ambitions of
the project are:
1. To improve the existing knowledge on the interaction between the matter and the THz
waves.
2. To build a terahertz laboratory infrastructure distributed among the different groups
participating in the project.
3. To establish a joint international graduated program on THz electromagnetic sensing
able to attract bright students from worldwide.
2
Chapter 1
Figure 1.1: TeraSense project logo.
4. To coordinate a joint public-private effort at national level and improve the presence
and projection of the Spanish technology at international levels.
5. To develop a real-time two-dimensional close-range camera for security applications
working at W-band.
6. To develop a remote sensor radar system working at 300 GHz able to perform atmospheric and environmental scanning.
7. To develop a near-field scanner for imaging and sensing of bio-structures and pharmacology working from 0.5 THz to 2 THz.
The research described in this thesis is linked with objectives 5 and 7 of the TeraSense project.
The first part of this document is devoted to the study of passive close-range Millimeter-Wave
(mmW) imaging systems whereas the second part explains the research on THz tomographic
imaging of pharmacological compounds, being both parts related with objectives 5 and 7
respectively.
1.2
State of the art
This section will place the work described in this thesis into the current research context in
the areas of mmW and THz systems with special focus on W-band passive imaging and THz
tomography.
1.2.1
Millimeter-wave technology and applications
The mmW frequency range is comprised from 30 GHz to 300 GHz. In such wide range, the
applications and technologies that are found in the lower frequencies can be considerably
different from the ones working close to 300 GHz. Figure 1.2 presents an schematic showing
the distribution of the electromagnetic spectrum and some applications. As shown in the
figure, the most significant commercial applications in the mmW range are the automotive
radar and the Wireless Personal Area Network (WPAN) (standard IEEE 802.15.3c).
The application areas found in the mmW range are communications, active remote sensing and passive remote sensing. The technology and current research in each area is summarized in the following points:
1.2 State of the art
3
Frequency
3 GHz 10 GHz 30 GHz 100 GHz 300 GHz 1 THz 3 THz
Wavelength
10 cm
1 cm
Microwaves
1 mm
100 mm
THz waves
mmW
Microwave oven
Radioastronomy
WPAN
100
1000
10
100
10
1
1
0.001
4
10
20
40
100
200
370-400
220-270
0.01
110-150
0.1
75-110
Bit rate [Gbits/s]
Automotive
Radar
400
0.1
0.01
1000
Attenuation constant [dB/km]
Radar
Mobile phone
Fr e q u e n c y [ G H z ]
Figure 1.2: Schematic with the distribution of the electromagnetic spectrum depicting the main applications in each frequency range. The atmospheric attenuation level is also shown pointing out the available
atmospheric windows.
• mmW communications: On the one hand, the 60 GHz mmW WPAN (IEEE 820.15.3c)
is being developed to provide medium and short range wireless communications with
a sort of advantages if compared with Bluetooth WPAN (IEEE 802.15.1) [1]. The
spectrum of the 60 GHz WPAN is allocated from 57 − 66 GHz (in Europe) allowing a
huge spectral capacity of the link. In addition, the 60 GHz presents higher atmospheric
attenuation than the lower microwave frequencies due to an oxygen (O2 ) absorption
line placed at around 60 GHz [2]. The high path loss can be seen as an advantage for
WPAN links since the interference between different systems or collocated networks
is reduced. Moreover, the frequency reuse capabilities and the spatial efficiency are
improved. An additional advantage is based on the size of the transceiver electronics.
As the frequency is increased the size of the transceiver components can be reduced.
Hence, the size of mobile or portable devices using 60 GHz WPAN can be shrunk. The
current research is divided in three main aspects: 1) the channel analysis and modeling;
2) the modulation scheme; 3) the broadband circuit technologies and 4) the reconfigurability of the antennas.
On the other hand, the Japanese government in collaboration with Nippon Telegraph
and Telephone Corporation (NTT) has developed the technology to transmit uncompressed High Definition Television (HDTV) video through a wireless link with a central frequency of 120 GHz. The link is capable of transmitting up to 10 Gbits/s and is
expected to be used in the last mile of 10 Gigabit Ethernet as well as for multiplexed
transmission of up to six channels of uncompressed HDTV video. In order to achieve
4
Chapter 1
such large bandwidth, NTT has developed technology to convert an optical subcarrier
data signal produced by photonics technology into electronic signals and radio waves
using Uni-travelling Carrier Photodiode (UTC-PD) [3, 4]. It provides the photonics
features such as wide bandwidth, good stability and ultrahigh frequency to generate
electromagnetic waves in the mmW range. Current research has been performed using Amplitude Shift Keying (ASK) modulations, however it is expected that data rates
up to 20 Gbits/s can be achieve if most sophisticated modulations schemes such as
16-state Quadrature Amplitude Modulation (16QAM) are used.
• Active remote sensing: The main application in the area of active remote sensing at
mmW frequencies is the automotive radar sensor [5, 6]. The radar is used as a driver
assistant for various functions such as adaptive cruise control, automatic emergency
braking and parking aid. The first generation of automotive radar sensors working at
77 GHz was introduced in 1998 by Daimler. Since then, several new generations of
sensors have appeared from a number of manufacturers all relying on the FrequencyModulated Continuous-Wave (FMCW) modulation technique. In Europe a total of
4 GHz are available for this purpose from 77 GHz to 81 GHz allowing a range resolution of 10 cm. The technology used to build the radar is usually based on Monolithic Microwave Integrated Circuit (MMIC) using GaAs semiconductor. Recently, implementations using 90 nm and 60 nm Complementary Metal-Oxide-Semiconductor
(CMOS) technologies have been published [7].
Taking advantage of the wide bandwidth available for radar purposes in the mmW
frequency region, other applications using radar techniques have appeared. As an example, in [8] a three-dimensional holographic imaging technique is shown to perform
personnel screening for concealed weapon detection purposes. In [C7], an interferometric system is shown capable of detecting surface deformations on the order of tens
of micrometers. Additionally, the W-band atmospheric window has been widely used
to perform active remote sensing of the atmospheric properties such as the cloud formation and composition [9] [10].
• Passive remote sensing: Radioastronomy is the application concentrating the main
efforts of the scientific community in the area of passive remote sensing. This effort is translated in examples like the Atacama Large Millimeter/Submillimeter Array (ALMA) international telescope [11]. It is situated on a dry place at 5000 m of elevation, allowing an excellent atmospheric transmission over the instrument frequency
range from 30 GHz to 1 THz. The radio telescope consists of two antenna arrays: one
of 64 antennas with 12 m diameter each being reconfigurable in multiple patterns ranging from 150 m to 15 km; and a second array consisting of a set of 4 antennas with
12 m diameter and 12 antennas with 7 m diameter working in packed configurations of
50 m diameter [12]. ALMA will provide total power and interferometric information
on molecular, atomic, ionized gas and dust in the solar system.
A second example of a mmW instrument developed by the radioastronomy community
the Planck radio telescope [13]. This instrument was launched in 2009 together with the
Herschel radio telescope. Planck covers a frequency range from 30 GHz to 857 GHz
and its objective is to map the entire sky by strip scanning with a spin rate of 1 rpm.
The mmW frequency range is also used to retrieve environmental parameters such as
1.2 State of the art
5
Figure 1.3: Artist view of a passive scanner portal that is capable to detect objects concealed beneath the
clothes. The working principle of this portal is to distribute in a vertical disposition a group of horizontal
passive arrays in such a way that a 2D image is obtained.
temperature, humidity and liquid water of the soil. In [14], total-power measurements
at mmW are used to retrieve the aforementioned parameters. Additionally, passive remote sensing combined with image formation techniques is applied to solve several
security issues: aircraft landing and guidance; low-visibility navigation and situational
awareness; reconnaissance and surveillance; search and rescue and drug interdiction
among others. An example can be found in a W-band radiometric imager that helps
in the landing process of an helicopter. It provides real time imaging through the dust
cloud when the helicopter is landing, thus reducing the probability of accident [15]. An
additional application of the passive imaging is the personnel screening for concealed
object detection. This application concentrates the research on mmW passive imaging presented in this thesis. The research undergoing in this area is described in the
following section.
1.2.2
Millimeter-wave passive imaging for personnel screening
Several companies have developed proprietary systems for concealed threat detection. These
systems are designed either in a walkthrough portal configuration as the one shown in Fig.
1.3 or for stand-off operation. Portal systems are usually designed to detect small threats at
short distances (< 3 m), achieving spatial resolutions around 1 cm whereas stand-off systems
are conceived for larger distances and larger threads. There are three different operating frequency ranges in use for personnel screening purposes: 1) 25 to 35 GHz; 2) 94 GHz; and 3)
200 to 300 GHz. Each corresponds to one of the windows that exist in atmospheric propa-
6
Chapter 1
(a) ThruVision T4000 passive scanning system
(b) Brijot MobileScanPS passive scanning system
Figure 1.4: Two examples of commercial passive scanning systems.
gation. Atmospheric absorption is not a significant issue for the relatively modest distances
used in people-screening applications, nevertheless by working in the same frequency ranges
as some of the longer distance applications it is possible to benefit from more readily available and lower cost components. At the lower frequencies, equipment needs to be relatively
large, or resolution is sacrificed. Higher frequencies enable more compact systems such as
those developed by ThruVision [16]. Also, specially for passive systems, it is easier to detect
dielectric threat materials at higher frequencies since their higher refractive indices at these
frequencies makes them appear more metal-like and reflective. Another compact system, operating at 94 GHz for modest stand-off distances has been developed by Brijot. Figure 1.4
shows two photographs of the systems commented in this paragraph.
A number of different scanning systems are in use with mechanical, electronic and hybrid
configurations. The Smiths Detection system uses a pair of spinning tilted mirrors to scan in
the x-axis and a third mirror to raster scan in the y-axis on to the detectors. The Qinetiq [17]
system uses a different arrangement with a single rotating mirror to produce a conical scan
on to a complete line array. It also exploits polarizers and a quarter-wave plate to enable a
folded optic reducing the dimensions of the scanning system.
The Trex Sago [18] approach is to create an azimuthal line scan through a frequency dependent coupling into an antenna. In the ST150, the second axis is provided by panning the
main reflecting mirror. In their real-time imager, a phased array of some 230 receivers is
deployed. The L-3 SafeView [19] system is an active system based on developments from
PNNL using a holographic reconstruction from a fan-beam source and line array of detector
antennas which rotate around the subject being scanned. This system measures both amplitude and phase of the reflected signal for use in the FFT-based holographic image reconstruction.
1.2 State of the art
7
A novel approach has been developed by Agilent [20] and demonstrated in prototype
form. This employs a confocal arrangement of a single source and detector. The source is
reflected from a configurable mirror made up of a 2-dimensional array of several thousand
dipole reflectors. Each dipole is connected to a large, fast switching array which can place
either a short or open circuit at the feed point of each dipole. This forms a programmable,
reflecting Fresnel zone plate which can be used to focus the millimeter wave source and
detector onto a chosen point in space in front of the mirror. The antennas can be switched
so as to scan over 107 pixels per second, leading to a solid state imaging system with a
15 Hz refresh rate or higher. Although the frequency employed is relatively low, 24 GHz in
the prototype system, the programmable mirror is only a few centimeter thick, leading to
relatively compact system.
Development directions in mmW systems focus largely on methods to reduce the cost of
systems, without sacrificing neither sensitivity nor resolution. Since most of these systems
use a number of detectors in order to be able to capture moving images, the cost of multiple
receivers dominates the total cost of the system.
1.2.3
Terahertz systems and applications
The THz frequency range is comprised between 300 GHz and 3 THz as shown in Fig. 1.2,
placed between the Radiofrequency (RF) spectrum and the infrared and optical spectrum.
Either photonic or electronic techniques are used to generate THz electromagnetic waves
depending on the type application.
There are mainly 4 ways of generating radiation in the THz range:
• In order to generate a local oscillator for a THz transceiver in the range between
300 GHz and 1 THz usually electronic techniques are used. In this case, a mmW phaselocked oscillator is upconverted to the desired frequency by a multiplier chain [21].
• If a broadband pulsed radiation is required (e.g to perform spectroscopy) usually a Photoconductive Antenna (PCA) is used [22]. By exciting the PCA using a femtosecond
laser pulse, a broadband THz pulse radiation is emitted [23]. The duration and therefore the spectral content of the emitted pulse depends basically on the duration of the
laser pulse and on the relaxation-time of the photocarriers created by the laser pulse on
the antenna semiconductor.
• To generate a Continuous Wave (CW) signal beyond 1 THz usually a Photoconductive Switch (PCS) is used [24, 25]. The signals coming from two lasers are mixed in
the PCS, giving an output frequency equal to the frequency difference between both
lasers. This technique usually gives a power with a order of magnitude lower than the
electronic generation, however it is suitable for higher frequencies.
• If a CW high-power source (around 30 mW) is required, the solution is given by a
Quantum Cascaded Laser (QCL) [26, 27]. This laser is a semiconductor device where
the light emission is obtained through intersubband transitions in the quantum wells.
This allows to radiate at lower frequencies than a typical optical laser. However the
output frequency range is restricted to frequencies greater than 1.5 THz.
8
Chapter 1
Depending on the power requirements, the frequency and the application one among the
aforementioned THz generation techniques should be chosen. The applications in the THz
range can be distributed in the following areas: 1) Communications; 2) Remote sensing; 3)
Spectroscopy and 4) Imaging
• Terahertz communications: The THz frequency range is very attractive for communications due to the huge available bandwidth [28]. However, the signal path loss is a
disadvantage. Figure 1.2 shows that atmospheric attenuation increases drastically beyond 100 GHz. Therefore, the research is focused on short-range Wireless Local Area
Network (WLAN) and WPAN systems applied to wireless displays, HDTV distribution, backhaul traffic, etc. In addition, THz communications may interfere with the
classical application of this frequency band: the radioastronomy [29]. This issue has
been recently investigated and is concluded that the transmitter should be kept 55 km
away from any radio telescope. Nevertheless, the research is still in an initial stage, and
no relevant transceiver demonstrators working beyond 300 GHz have been published.
• Active and passive remote sensing: As in the mmW frequency range, the main application for passive remote sensing in the THz range is the radioastronomy. An example
is the Herschel radio telescope launched to the space in 2009 [30, 31]. The HIFI instrument carried by Herschel can retrieve a total power information of the sky in two
polarizations over seven frequency bands between 480 GHz and 1.91 THz. Herschel
has a cassegrain reflector antenna system with a main reflector of 3.5 m diameter and
the instruments are cooled down to 80 K. The measurements are used by the scientific community to discern the weak signals from distant galaxies and to resolve among
multiple forming stars and galactic clouds.
On the other hand, the THz range is not widely used in passive remote sensing for security applications since the sensitivity of the available receivers beyond 300 GHz does
not allow the acquisition of images in real-time. In order to improve the acquisition
time, active approaches have been developed. An example is a FMCW radar developed
by the Jet Propulsion Laboratory (JPL) of the National Aeronautics and Space Administration (NASA) [32] [33]. The system can acquire three-dimensional images at a
standoff distances of 25 m in five seconds operating at 675 GHz. It relies on a 1 m diameter ellipsoidal main reflector to achieve an spatial resolution of around a centimeter
at 25 m range.
• Spectroscopy: Many materials presents vibrational or rotational modes at molecular
level in the THz frequency range. This is translated in an absorption of the electromagnetic energy at the resonance frequency. In order to measure absorption frequencies,
a broadband THz emission is produced and directed to the material. The absorption
spectra of the received signal is analyzed to find absorption peaks. An absorption spectrum can completely characterize a material, therefore a certain material can be detected
and its concentration can be calculated from an spectroscopic analysis [34, 35].
The most extended THz spectroscopy system is the Terahertz Time-Domain Spectroscopy (THz-TDS). It relies on PCA to emit and receive the THz radiation and a
femtosecond laser is used to excite the PCA. The amplitude and phase of the emitted
pulse can be measured by sampling the THz pulse by using a delay stage that controls
1.2 State of the art
9
Schematic
Spectrographic / tomographic Imaging
PC
Acq.
Receiver
λ/2
λ/4
Sample
under
test
Delay
Emitter
THz
Emitter
Retina
THz
Receiver
Femtosecond Pulsed Laser
Delay line
• Spectral Range (min.) - 0.1-3 THz
• Dynamic Range - >50 dB (typ 60)
• Scan Range - 300 ps
• Repetition Rate - 100MHz
• Wavelength - 780 nm
• Pulse Duration - 100 - 120 fs
• Output Port • Total Average OutputP- >65 mW
Figure 1.5: Schematics of a THz-TDS system with accessories to perform tomographic imaging (e.g. a
rotor used to rotate the sample and a retina used to multiplex multiple points of view without necessity
of mechanical movements). The main parts that intervene in the emission and reception of the THz
pulse are depicted.
the delay of the laser pulse. With this measurement system, the refractive index and the
absorption coefficient of the material sample can be retrieved.
• Imaging: Recently, a real-time CMOS camera has been published [36] [37] [38]. It
consists on a 1 kPixel THz detector fully integrated in a 65 nm CMOS technology
and it is capable of capture real-time video with up to 500 fps. The design achieves
a bandwidth from 790 GHz to 960 GHz. This camera presents a great advance in the
THz technology since it represents a cheap, compact and reliable instrument to acquire
images in the THz range.
Terahertz microscopy is also being developed and has been already applied to image
semiconductor devices achieving down to 150 nm of spatial resolution [39]. The technique is based on capturing the near-field reflected by the sample using a very thin field
probe. In this case the diffraction effect does not limit the resolution since the electromagnetic field has not been propagated, and therefore it has not lost information that
limits the resolution in typical imaging.
Additionally, THz imaging techniques are being developed to perform 3-dimensional
imaging of biological, pharmaceutical and alimentary samples [40, 41]. The imaging
information can be combined with the spectroscopic information to detect different
materials dispersed over a sample. The following section describes in detail the current
research on THz tomography.
10
1.2.4
Chapter 1
Terahertz spectroscopy and tomography
Terahertz tomography refers to imaging by sections through the use of THz electromagnetic
waves. Two main classifications of tomographic techniques are found in the literature: the
diffractive techniques [42] and the non-diffractive techniques [43].
The diffractive techniques are based on illuminating the sample with an electromagnetic
wave and measure the scattered field. From the measured information the currents that have
been excited on the sample by the emitted field can be reconstructed, and thus the shape of the
sample can be retrieved. The expressions that govern this method emanate from the Maxwell
equations and cannot be solved analytically. In order to solve the expression for the scattered
field, an approximation should be used. There are mainly two approximations to solve the
problem: the Born approximation [44] and the Rytov approximation [45].
The Born approximation was introduced by Max Born in 1925. If the scattered field is
much smaller compared with the incident field, the scattered field can be expressed by its
first order approximation. The Born approximation can be applied if d∆n < λ4 where d is
the target size and ∆n is the index of refraction difference between the air and the sample.
From this approximation, one can observe that the approximation can be applied when the
wavelength is several times the size of the object. Hence, in the THz frequency range the use
of this approximation is unusual since the wavelength is usually smaller than the object.
The Rytov approximation assumes that the incident field is perturbed by the sample only
by introducing a phase shift along its propagation path. This approximation is considered
more accurate than the Born approximation and it should provide a better estimate of the
scattered wave. In addition, the approximation condition is less restrictive than the condition
in the Born approximation and it just requires a slow variation of the refraction index of
the sample over a wavelength. Additionally, Rytov approximation also has a better behavior
when the measuring wavelength is longer than the sample.
There are not many research publications using the aforementioned algorithms in the THz
range since usually the conditions are not fulfilled and the resulting images do not reconstruct
the shapes of the sample. The reconstruction algorithm commonly used in THz tomography
is a non-diffractive method inspired from the x-ray: Computed Tomography (CT). The attenuation produced in the incident field by the object can be described by a line integral of the
object function along its path called Radon transformation
Z
P (θ, t) =
f (x, y)dl = R(f (x, y)),
(1.1)
L(θ,t)
where P (θ, t) is the attenuation function of the incident ray along the path l, and t is the
ray minimum distance from the sample origin. The attenuation function can be measured by
rotating the the object along θ and by sweeping the position of the ray along a line in order to
obtain multiple samples on t. Hence, f (x, y) can be retrieved by applying the reverse Radon
transformation to the measurements. In practice, a THz beam cannot be treated as a ray line
as in in the x-ray CT. Therefore special attention should be taken to create a measurement
environment where the assumptions of CT are still valid. The beam should be focused in the
sample by using either lenses of parabolic mirrors. The resolution of the image cannot be
better than the waist of the beam synthesized by the focusing element. Moreover, the sample
1.3 Objectives and scope of the thesis
11
Objectives
mmW close-range passive imaging
Preliminar work
mmW close-range
measurements
with TPR
Close-range
mmW passive
system performance
Improve the
correlation method
of large bandwidth
radiometric signals
applied to mmW
asessment and
study
interferometry
Terahertz tomography and spectroscopy
Introduction
to the THz systems
and the tomographic
method
Scene
simulation and
assessment of the
tomographic
algorithm
Validation
of the method
by imaging samples
with known spectral
fingerprint
Figure 1.6: Diagram showing the main objectives of both the mmW and THz parts of this thesis.
should be small enough to fit in the focus depth of the beam, otherwise the size of the beam
will vary along the sample and the assumption of rays is not further valid.
The spectroscopic information appears directly in the reconstructed result by using all the
aforementioned methods [46,47]. By using a THz-TDS system to measure the multiple point
of views, the full spectral information of the sample is obtained. Therefore, the reconstructed
image can reveal the different materials contained in the sample analyzing the spectrum.
Figure 1.5 shows a THz-TDS system with the main components (e.g. femtosecond laser, two
PCA, delay stage,...). This system is used, among other applications, to perform tomography
of small samples. The dynamic range is around 65 dB in present commercial systems and its
main advantage is that it can measure the complete THz spectral range at real time.
1.3
Objectives and scope of the thesis
At the beginning of the research work in this thesis, the state of the art for the two main
topics described above were analyzed to identify lacks or deficiencies. From the conclusions
on the literature survey, the objectives stated in this section were chosen. A main division
of the objectives has been done between the objectives that appear in this thesis and the
ones that have been considered out of the scope. In addition, the objectives have been subdivided in two lists, the first related with mmW passive imaging and the second related with
THz imaging. Each objective is related with its corresponding paper contribution either in a
conference [Ci] or in a journal [Ji].
12
Chapter 1
1.3.1
Objectives appearing in this document
A summary of the objectives appearing in this document is presented in Fig. 1.6 depicting
the timeline distribution among the objectives.
• Millimeter-wave passive imaging
– Passive imaging introduction and imaging: A simple demonstrator is built to
test the passive imaging capabilities in indoor and outdoor conditions [C6, C8,
C12].
– Close-range passive imaging performance analysis: A complete theoretical
comparison including simulations of the close-range behavior of three radiometers in order to detect optimum configurations that can achieve better performance
with lower overall cost [J2].
– Correlation method for large bandwidth radiometric signals: An optical correlation method is applied for correlating large bandwidth radiometric signals
coming from mmW interferometric radiometers [C3, C4] [J1].
• THz spectroscopy and tomography
– Diffractive spectroscopic tomography: A tomographic algorithm based on the
Born approximation is applied to retrieve spectroscopic images. The spectral
information of each pixel can be obtained to identify different compound types
in the same image. Most of the THz tomographic systems use CT methods to
retrieve the image and the diffractive techniques are not studied in deep in the
literature [C1].
1.3.2
Objectives excluded from this document
• mmW systems and components:
– Assessment of THz active Mills-Cross imaging: By placing two W-band headers from a Vectorial Network Analyzer (VNA) into two linear stages an active
Mills-Cross setup is built. Measurements are obtained to assess the suitability of
this imaging geometry in the mmW range. [C14–C16].
– Radiation pattern characterization of a mmW Cassegrain reflector: The radiation pattern of a Cassegrain has been characterized from near-field measurements. In addition, the return loss parameter has been adjusted by using a matching section formed by adjustable screws [C2].
• THz imaging:
– Terahertz subsurface imaging system: By using a portable THz-TDS system,
subsurface images of a ceramic sample are obtained with resolutions around
0.3 mm [C13].
1.4 Organization of the document
1.4
13
Organization of the document
This document has been divided in 4 main parts: 1) the introduction; 2) the research on
mmW passive systems; 3) the research on THz tomographic imaging techniques; and 4)
conclusions and further discussion. The second part is sub-divided in three chapters whereas
the third part is concentrated in one chapter. Each chapter has an introduction or abstract at
the beginning followed by a description of the general concepts required to understand the
core of the chapter. Measurement or simulation results are found at the end of the chapter and
are used to validate the theoretical approach of the problem developed in the core of chapter.
At the end of each chapter, with exception of the present one, the conclusions of the obtained
results are written.
The second part, Close-range Millimeter-wave Passive Imaging, is devoted to describe
the advances achieved in the field of the mmW radiometry. The second chapter includes a
total power and interferometric radiometry introduction. Furthermore, it includes a complete
design of a total power radiometer used to study the behavior of the mmW components as
a previous step to design the interferometric radiometer shown in the third chapter. Indoor
and outdoor close-range measurements of persons with concealed objects are shown to study
the detection capabilities of the system. The third chapter describes a theoretical study and
comparison of three types of screeners and their behavior in close-range imaging: the RealAperture (RA) radiometer, the One-Dimensional Synthetic Aperture (1D-SA) and the TwoDimensional Synthetic Aperture (2D-SA). The fourth chapter and the last one of the second
part of this thesis is devoted to describe a method developed to correlate radiometric signals
in the optical domain. Measurements of the system are shown validating the suitability of the
method for passive mmW interferometric imaging.
The third part, Terahertz Imaging and Spectroscopy, is devoted to describe the tomographic and spectroscopic imaging research performed in this thesis. The fifth chapter, introduces the terahertz imaging basic concepts, presents simulations of the method that is applied
and finally show measurements validating the method.
The last part concludes the document and presents further discussion on the achievements
of this thesis.
14
Chapter 1
Close-Range Millimeter-Wave
Passive Systems
C HAPTER 2
Millimeter-wave radiometric imaging
the first part of this chapter the Millimeter-Wave (mmW) radiometry fundamental concepts are described as an introduction for Chapters 3 and 4, paying special attention to
the Synthetic Aperture (SA) interferometric radiometry. In the second part of this chapter,
design and assembling details of a Total-Power Radiometer (TPR) are explained with the aim
of introducing the mmW radiometry from a practical approach. The development of a TPR
has been convenient to explore the particularities of mmW components and to acquire the
experience to perform the practical work shown in Chapter 4. In addition, several radiometric
images obtained with the TPR in different environments are shown, providing examples of
concealed object detection capabilities of mmW radiometry.
I
N
2.1
Millimeter-wave radiometry
Radiometry is defined as the science devoted to measure the electromagnetic thermal radiation
emitted by an object having a temperature higher than 0 K. It was originally developed by the
astronomy community to measure the natural radiation produced by cosmic bodies. In the
microwave frequency range, an example of radiometric application is the sensing of physical
parameters of the Earth such as ocean water salinity levels and soil moisture [48], where the
geophysical parameters are related with the levels of thermal emission. At mmW frequencies,
the passive close-range imaging for concealed object detection has been developed during
the last decade, providing images related with the temperature contrast among bodies in the
imaged scene. The latter application is the research focus in the following chapters, therefore
this section gives a basic introduction of the main concepts that govern the radiometric science
with special emphasis in the behavior at the mmW frequency range.
18
Chapter 2
B b[Wm −2sr −1Hz −1]
10
10
10
10
10
−8
Plank law
Rayleigh−Jeans law
−12
−16
−20
−24
10
7
10
9
11
10
f [GHz]
10
13
10
15
Figure 2.1: Spectral brightness Bb of a black-body with a physical temperature Tph = 300 K
calculated using the Planck’s law (2.1) and the Rayleigh-Jeans approximation (2.2).
2.1.1
Thermal radiation and Plank’s law
In order to describe the parameters that quantify the thermal radiation of an object, first the
concept of black-body should be introduced. It consists of an ideal physical body that, in
thermodynamic equilibrium, absorbs all incident energy and re-emits all absorbed energy.
The spectral brightness Bb (the radiated power density per unit solid angle, per unit area and
per Hertz) of a black-body at a physical temperature Tph is quantified by the Plank’s law
Bb =
2hf 3
1
c2 e kBhf
Tph
−1
[Wm−2 sr−1 Hz−1 ],
(2.1)
where h is the Planck’s constant, kB is the Boltzmann constant, f is the radiation frequency
and c is the speed of light. The exponential function appearing in the Planck’s law can be
approximated by the first order Taylor polynomial if f khB Tph . The resulting expression
is the Rayleigh-Jeans law
Bb =
2kB f 2
Tph
c2
[Wm−2 sr−1 Hz−1 ].
(2.2)
This expression is valid if f 6 THz for a black-body with a physical temperature Tph =
300 K (around ambient temperature). Hence, since the radiometric research presented in the
following chapters has been performed at W-band (75 − 110 GHz) and at room temperature,
the Rayleigh-Jeans approximation is used instead of the Plank’s law for the sake of simplicity.
Figure 2.1 shows the spectral brightness Bb of a black-body with a physical temperature
Tph = 300 K in logarithmic scale, where can be stated that the Rayleigh-Jeans law is a good
approximation of the Planck’s law for mmW frequencies.
2.1.2
Antenna surrounded by a black body
A radiometer is the name given to the electronic receiver device used to measure the thermal
radiation power emitted by a body. The received power by the radiometer with bandwidth B
2.1 Millimeter-wave radiometry
19
Enclosure
Absorber
Thermal
Radiation
Antenna
Pr
Figure 2.2: Schematic representation of an antenna surrounded by a black-body.
centered at f0 is calculated by integrating the spectral brightness of the black-body along the
frequency bandwidth and along a sphere. In an ideal case, when the radiometer antenna is
surrounded by a black-body with constant Tph as shown in Figure 2.2, the received power is
Pc =
1
Ae
2
f0 + B
2
Z
f0 − B
2
Z Z
4π
2kB f 2
Tph t(θ, φ)dΩdf = kB Tph B
c2
(B f0 )
[W],
(2.3)
where Ae is the antenna effective area and t(θ, φ) is the normalized antenna power pattern.
The concept of antenna temperature TA can be defined from the result in (2.3) as the temperature of an ideal black-body that would result in the same received power at the antenna
aperture as in the actual case. Therefore, in an ideal receiver, the antenna temperature can be
calculated as TA = Pc /(kB B).
2.1.3
Gray body radiation and apparent temperature
Real objects do not behave as black-bodies but as gray-bodies. They differ in the sense that
gray-bodies do not absorb all the incident radiation because part is reflected, and therefore
only part of the incident energy is re-emitted. In addition, the radiation emitted by graybodies is not omnidirectional and thus, the radiation angular distribution should be taken into
account. The spectral brightness of a gray-body Bg is expressed as
2kB f 2
TB (θ, φ),
(2.4)
c2
where TB is the brightness temperature associated to the spectral brightness of the gray-body.
The brightness temperature is related with the physical temperature by the material emissivity
e as
TB (θ, φ)
e(θ, φ) =
.
(2.5)
Tph
The emissivity depends on the material and several parameters such as temperature, emission
angle and frequency. The Kirchhoff’s law of thermal radiation states that, in thermal equilibrium emissivity equals absorptivity. Hence an object that does not absorb all incident energy
Bg (θ, φ) =
20
Chapter 2
Material
Explosive
Metal
Skin
Denim
T-shirt
Emissivity
100 GHz 500 GHz
0.74
0.95
0
0
0.65
0.91
0.09
0.49
0.04
0.2
Reflectivity
100 GHz 500 GHz
0.26
0.05
1
1
0.35
0.09
0.01
0.01
0
0
Transmissivity
100 GHz 500 GHz
0
0
0
0
0
0
0.9
0.5
0.96
0.8
Table 2.1: Emissivity, reflectivity and transmissivity of typical materials
related with radiometric security imaging [49].
will emit less power than a black-body. From this statement arises the relation among the
emissivity e, reflectivity r and transmissivity t concepts:
e + r + t = 1.
(2.6)
Table 2.1 shows the emissivity, reflective and transmissivity values of various materials related with human body security imaging at 100 GHz and 500 GHz. When a gray-body is
placed in a complex environment with other objects surrounding it, the power coming from
the gray-body is not only related with its physical temperature. There are two additional effects that are included in the measured power coming from the body: 1) the reflected energy
on the body surface; and 2) the energy that penetrates the body and is transmitted thorugh it.
The total measured power is related with an apparent temperature TA seen from the body
TA = eTph + rTbr + tTbb ,
(2.7)
where Tbr is the brightness temperature of background which is reflected by the object and
Tbb is the temperature of the background behind the object.
2.1.4
Image temperature contrast
The power received by a radiometer coming from a body does not only depend on the body
physical temperature but also on its absorption characteristics and the environment brightness temperature. Therefore the temperature contrast in an image acquired by a radiometer
will strongly depend on the environment when imaging objects that are not purely absorptive.
Table 2.1 shows that the usual object materials found in a security scene have a reflectivity
coefficient greater that 0.2 and in the limit, metal objects have a r = 1. Hence, the temperature contrast of objects that usually appear in security scenarios will strongly depend on the
reflected radiation coming from the environment. In security image two types of scenarios,
the indoor and the outdoor, are defined due two their different characteristics of background
brightness temperature distribution. Figure 2.1.4 shows an artist view with the background
radiation characteristics of both scenarios.
The outdoor scenario is represented in Fig. 2.3(a) where three different background radiations are depicted: 1) the sky radiation has a brightness temperature of around Tsky = 100 K
at mmW frequencies, although it depends on various parameters such as the incidence angle
2.2 Total-power radiometer with mechanical beam-scanning
(a)
21
(b)
Figure 2.3: Artist views of an outdoor scenario (a) and an indoor scenario (b) depicting the
background temperatures that affect the result of the image contrast.
and the cloud density; 2) the brightness temperature of the floor Tfloor is related on its physical temperature that will depend on the quantity of absorbed solar radiation; and 3) the scene
brightness temperature Tscene depends on the ambient temperature. The effect of each background radiation is different on the each image portion. The sky temperature is reflected on
the shoulders and on metallic objects appearing very cold in the image. The opposite effect is
found from the knees to the feet, where the floor radiation is reflected appearing warmer than
the rest of the human body. As a result, usually the images have a temperature gradient from
cold to warm going from the head to the feet.
Figure 2.3(b) corresponds to a indoor scenario where the brightness temperature of the environment Tscene is usually homogeneous and related to the ambient temperature, hence the
effect on the image is uniform. The main difference between indoor and outdoor scenarios is
the contrast level on the image. Outdoor scenarios experience higher contrasts since the reflection of the sky in the objects increase their apparent temperature difference. The dynamic
range of the image also increases and goes from around 100 K to the ambient temperature
(≈ 300 K). In an indoor scenario, the contrast is poor since the ambient temperature is very
close to the body temperature and the dynamic range of the images is of around 20 K. In this
case the radiometer should be more sensible in terms of received brightness temperature to
be able to detect small changes in temperature. For a radiometer with a certain radiometric
sensitivity indoor images are noisier than outdoor images and the detection capabilities are
reduced in indoor scenarios. Measured images presented in section 2.2.6 are a good example
to examine the aforementioned contrast differences.
2.2
Total-power radiometer with mechanical beam-scanning
The TPR is a basic radiometer receiver that collects the scene radiation by using an antenna,
filters and amplifies the Radiofrequency (RF) signal and detects its power by using a device
22
Chapter 2
Antenna
ni(t)
Bandpass
filter
Amplifier
Power detector
Integrator
nr(t)
Vo=Pr
Figure 2.4: Block diagram of the basic components of a TPR.
with a quadratic response. The final step is to average the signal at the output of the power
detector in order to improve the Signal to Noise Ratio (SNR). Figure 2.4 shows a simplified
block-diagram of the radiometer components. The TPR is the most common radiometer due
to its simplicity and is the one chosen to introduce the basic radiometry concepts that will
appear along the document.1
The voltage noise signal at the input of the power detector nr (t) can be modeled as
nr (t) = nIr (t) cos (ωt) − nQr (t) sin (ωt)
[V],
(2.8)
where Nr (t) = nIr (t) + jnQr (t) is the equivalent baseband of the input noise. The phase and
quadrature components, nIr (t) and nQr (t) respectively, are independent stochastic processes
with Gaussian probability density function and standard deviation σ. Hence, if a unitary
resistor is considered at the input of the power detector, the voltage value at the output of the
integrator is
Vo = E kNr (t)k2 = 2σ 2 = kB GBTsys
[V],
(2.9)
where E{} is the expectation operator and G is the gain of the amplifier. The system temperature Tsys = TA + TR includes the contribution of the noise added by the receiver TR to
the input noise. The receiver noise temperature TR depends on the Noise Figure (NFI) of the
receiver (usually fixed by the first amplifier) and can be calculated as TR = 290(NFI − 1).
The parameter B is the equivalent noise bandwidth of the bandpass filter defined by
Z ∞
1
B=
|H(f )|2 df
[Hz],
(2.10)
Hmax 0
being H(f ) the frequency response of the filter and Hmax its maximum value. The measurement standard deviation gives an estimation of the sensitivity of the system and can be
calculated as
s
2
E {kNr (t)k4 } − E {kNr (t)k2 }
2σ 2
std(Vo ) =
=√
[V],
(2.11)
N
N
where N is the number of independent samples taken in the integration being equivalent to
N = Bτ where τ is the integration time. From (2.9) and (2.11) the radiometric sensitivity in
terms of temperature resolution can be defined as
Tsys
∆TN = √
Bτ
1 The
[K]
following paragraphs of this section may contain verbatim text and figures from [C6, C8, C12].
(2.12)
2.2 Total-power radiometer with mechanical beam-scanning
23
Ideally, ∆TN can be arbitrarily low if the integration time is increased. However, the gain
variability of the components in the receiver chain strongly reduces the sensitivity of the
measurement. This is the main drawback of the TPR and can be solved using compensation
techniques such as Dicke switching [50]. The effect of the gain variability on the system
temperature is expressed as
∆G
[K],
(2.13)
∆TG = Tsys
G
being independent from the noise statistics. The receiver sensitivity taking into account the
gain uncertainty is given by
q
∆T = ∆TN 2 + ∆TG2 = Tsys
s
1
+
Bτ
∆G
G
2
[K],
(2.14)
The gain instability strongly increases ∆T reducing the radiometric sensitivity of the TPR.
Usually, a thermal control is required on the radiometer components to minimize gain fluctuations. When acquiring an image, the fluctuation impacts along the whole image acquisition
reducing the sensitivity. If no calibration is performed during the acquisition, the relation
between brightness temperature and received power will vary from the first acquired pixel to
the last one, yielding a distorted temperature map.
2.2.1
Total-power radiometer system design
A mmW TPR has been designed to evaluate the passive imaging performance at W-band.
The receiver architecture of the TPR is presented in Fig. 2.5(a) is based on a double-sideband
heterodyne receiver with 64 dB gain. The NFI of the radiometer is mainly fixed by the first
Low-Noise Amplifier (LNA), the 1.5 dB of the isolator losses and the phase noise introduced
by the Local Oscillator (LO).
A horn antenna is followed by an isolator that prevents the noise produced by the first
LNA to be radiated by the radiometer. After the isolator, two LNA stages feed the W-band
mixer achieving a chain gain of 64 dB. The LO of the system is based on a 15.16 GHz PhaseLocked Oscillator (PLO) multiplied by 6 using a W-band multiplier. A LO signal of 91 GHz
is mixed with the input noise signal, overlapping the RF bands from 88 GHz to 91 GHz and
from 91 GHz to 94 GHz, since the baseband bandwidth of the system is 3 GHz.
The baseband noise power is directly measured using a power detector that provides
an output voltage proportional with the input Root-Mean-Square (RMS) voltage. The output/input relation is calibrated and expressed by Vo = 7.7V/Vrms . The video bandwidth of
the detector is fixed to 2 kHz, however the signal is further averaged using a microcontroller.
Therefore, the video bandwidth of the receiver can be selected by changing the averaging
time in the microcontroller.
The receiver temperature is stabilized by using a Proportional-Integral-Derivative (PID)
controller with 3 heating resistors, 2 fan-coolers, 1 PT100 temperature sensor and 6 digital
temperature sensors. Figure 2.5(b) shows a photograph of the radiometer with the parabolic
reflector mounted on the pan-tilt scanner system.
24
Chapter 2
Mixer
Δf: 90-95 GHz
AD8361
IF: 0.1-2 GHz
LO Power 13 dBm RMS power detector
Conv. Losses: 8 dB Δf: DC-2.7 GHz
Conical Horn Antenna /
Waveguide Termination
PIC18F2550
µC data and
temperature
acquisition,
digital
averaging
A/D
Converter
LNA
ISOLATOR
G: 32dB
IL=1.5dB
ISOLATION 20dB Δf: 90-98 GHz
LNA
G: 32dB
Δf: 90-98 GHz
x6
TI-AD8344 16 bits A/D
Frequency multiplier
Max. Output power: 15dBm
Δf: 91-93 GHz
High pass filter
2 x K band
waveguide transitions
220 to 15V
Switched PS
8A max.
XP POWER – JPM120PS15
PID
Temp. Control
HITTITE HMC535LP4
Max. Output power: 9dBm
Δf: 14.7-15.4 GHz
x64
Reference oscillator
OX6749A-LZ-1
10MHz
PLO
6 x temperature
sensors
MAXIM – DS1820B
Synth.
ADF4360-7
N-Synthesizer
240 MHz
3x 10W Resistors
USB INTERFACE TO PC
Below 15.5 GHz
1x PT100 Sensor
94GHz components
Power Supply and Temperature Control
EUROTHERM 2132
2x FAN Coolers
(a)
(b)
Figure 2.5: (a) Receiver schematic and hardware components of the TPR.
(b) Photograph of the total power radiometer with the scanning system.
2.2.2
Calibration
The radiometer has been calibrated using a method based on measuring a temperature sweep
of a resistor block. The parabolic mirror is aimed sequentially to a resistor block and to an
absorber with fixed temperature in order to compensate gain fluctuations of the receiver. In
each measurement the resistor temperature is modified, starting with 100 ◦ C and reducing the
temperature in different steps down to 30 ◦ C, obtaining 7 calibration points plus 7 reference
points. An infrared camera together with a K thermocouple sensor are used to measure the
temperature of both the absorber and the resistor block.
The relation between receiver power and brightness temperature of the scene is given by
TB = aPo + b,
(2.15)
where the parameter TB ≈ Tph is the brightness temperature of the resistor block (where e
has been considered 1), b basically depends on the receiver noise temperature and Po is the
corrected received power. The proportional constant a depends basically on the Boltzmann
constant, the bandwidth of the receiver, the gain of both LNAs and the losses of the mixer.
The correction of the received power is performed by multiplying the measured power the
ratio between the reference measurement Pref and the absorber measurement Pabs yielding
Po =
Pref
Pr .
Pabs
(2.16)
Finally, the a and b parameters are obtained by inverting the simultaneous equations obtained
2.2 Total-power radiometer with mechanical beam-scanning
25
Antenna temperature [K]
400
350
300
Regression curve
Calibration points
250
152
152.5
153
153.5 154 154.5 155
Received Power [mW]
155.5
156
Figure 2.6: TPR calibration curve.
from 7 measurements

Pc1
P
a
 c2
= .
b
 ..
Pc7
+  
Tb1
1
Tb2 
1
  
..  ·  ..  ,
.  . 
1
(2.17)
Tb7
where the symbol ” + ” denotes the pseudoinverse of the matrix. The calibration result curve
is depicted in Fig. 2.6 having a calculated variance of 0.24 K.
2.2.3
Performance Assessment
√
The radiometric resolution ∆T in K/ Hz of the radiometer has been characterized by measuring the radiometer output response,
√ based on the ratio between the power detector output
voltage spectral density ∆V in V/ Hz and the power detector output Direct-Current (DC)
voltage VDC .
Two different regimes exist in the radiometer response separated by the so-called cornerfrequency. In the low frequency region the 1/f noise produced mainly by gain fluctuations in
the receiver chain
p predominates whereas in the region beyond the corner-frequency ∆V /VDC
converges to 1/(2B) in the case of using a linear power detector [51].
The characterization of the first region gives an information of the radiometer response
drift for long radiometer acquisition times (e.g. the acquisition of an image). If no calibration
is performed during the acquisition of an image, the ∆T will depend on the radiometer stability and thus on the output 1/f noise, as described in [52] [53]. However, if the radiometer
is calibrated at a faster frequency rate than p
the corner-frequency (e.g. with a Dicke switch),
the ∆T is constant with a relative value of 2/BRF . In this case, the relation between ∆V
and ∆T is given by
∆T
∆V
=2
.
(2.18)
Tsys
VDC
In order to obtain ∆V , the output voltage frequency spectrum of the detector has been
acquired and normalized by the video bandwidth with a HP 3561A Dynamic Signal Ana-
26
Chapter 2
−4
10
-1/2
VAC / VDC [ Hz ]
Spurious tones created by
fan coolers
−5
10
−6
10
1
10
Band filtered digitally by
the microcontroller
2
10
f [Hz]
3
10
Figure 2.7: Measured radiometer response spectrum against video frequency.
lyzer. The measurements have been performed with the radiometer input terminated with a
temperature controlled matched load at a temperature of 298 K. Figure 2.7 shows the measured ∆V /VDC for video frequencies between 10 Hz and 1 kHz, corresponding to frequencies
beyond the corner-frequency.
1
The ∆V /VDC is flat from 10 Hz to 100 Hz with a mean value of 12.9 · 10−6 Hz− 2 , giving
equivalent noise RF bandwidth BRF of 3 GHz. Beyond 100 Hz, spurious tones created by
the cooler fans appear. A better isolation between power supplies of the fans and the RF
circuitry should be performed to avoid this effect. Nevertheless, the radiometer is operated
with integration times greater than 1 ms, canceling√
these spurious signals. As a final result,
the computed ∆T from 10 Hz to 100 Hz is 83 mK/ Hz.
2.2.4
Description of the antenna system
The antenna system mounted on top of the radiometer is shown in Fig. 2.8(b). A 90◦ -offset
parabolic reflector with 100 mm of diameter and a focal distance of 152 mm has been used
to enhance the spatial resolution of the imaging system. Moreover, it has been mounted on a
pan-tilt scanner to acquire images at close standoff distances. The scanner is moved by two
servo motors, one per each axis, yielding a rotation resolution of 0.15 ◦ for both axes. The
reflector is fed by a horn antenna placed at 192 mm from the reflector. Adjusting the feeding
point further away from the reflector focal distance allows a proper near-field focusing at 1 m.
An approximated value of the angular resolution (-3 dB) is given by ∆θ = λ/D for an
uniform illumination, where λ is the wavelength at the center RF frequency of 91 GHz and D
is the diameter of the reflector. From this equation, 1.9 ◦ of beamwidth is obtained, translated
to 3.3 cm at 1 m standoff distance.
Figure 2.8(a) shows a simulation of the radiation pattern of the radiometer antenna. In
order to obtain the radiation pattern of the horn-reflector group, two simulation steps have
been followed: the first step is obtaining the radiation spherical modes of the horn using a
Method of Moments (MoM) simulation; and the second step is to use the spherical modes of
the horn as a point source in a Physical Optics (PO) simulation of the reflector.
2.2 Total-power radiometer with mechanical beam-scanning
Normalized Amplitude [dB]
0
27
E−plane
H−Plane
−5
−10
−15
−20
−25
−30
−35
−40
−10
−8
−6
−4
−2
0
[deg]
(a)
2
4
6
8
10
(b)
Figure 2.8: (a) Simulated radiation pattern of the radiometer antenna when focusing at 1 m.
(b) Photograph of the antenna system specifying the main components.
The simulation results show a beamwidth of 2.28 ◦ , slightly wider than the theoretical
since the taper caused by the horn illumination produces a reduction of the incident power at
the edge of the reflector of 10 dB. This effect reduces the angular resolution of the antenna
but improves the beam efficiency. The resulting beam efficiency ηb has been calculated as
R 2π R θb
t(θ, φ) sin θdθdφ
ηb = R02π R0π
,
(2.19)
t(θ, φ) sin θdθdφ
0
0
where t(θ, φ) is the normalized power pattern of the antenna system and θb is half of the
beamwidth of the antenna. This calculation gives the ratio of power received by the imaged
pixel over the total power received, achieving a 94 % for the current antenna system. It has to
be pointed out the importance of the beam efficiency in our system, since either the spillover
at the reflector or sidelobes effects caused by a sharp taper drastically increases the radiometer
acquisition error.
2.2.5
Beam distortion
In order to assess the distortion effect produced by the incidence angle and by the displacement of the reflector focus when aiming in elevation, the measurements shown in Fig. 2.9
have been performed. A resistor panel has been placed behind an absorber material having
a hole of 1 cm of diameter, thus creating a hot spot. Two images have been obtained at 1 m
distance: Fig. 2.9(a) shows an image of the hot spot when it is centered in the scene; additionally, a second image presented in Fig. 2.9(b) is acquired when the hot spot has been displaced
to the coordinates (0.4, 0.4) m in the scene, thus having the beam an incidence angle of 22 ◦ .
Two effects are observed when aiming to the border of the scene in Fig. 2.9(b), both
the dynamic range of the image and the spatial resolution are worse than in Fig. 2.9(a).
Specifically, the spatial resolution increases from approximately 4 cm to 6 cm due to the
beam distortion. Moreover, the dynamic range is reduced by 15 K since the beam efficiency
is reduced.
28
Chapter 2
(a) Centered point source
(b) Displaced point source
Figure 2.9: Acquired point source images to assess the beam distortion when aiming to the scene limits.
2.2.6
Imaging Performance
The radiometer performs a continuous raster scan in elevation and a step scan in azimuth.
For each pixel position, the radiometer microcontroller performs the desired integration of
the signal provided by the power detector and sends the value via Universal Serial Bus (USB)
to the computer. The computer software synchronizes the reflector aiming position with the
power acquisition and stores the information in a 3-dimensional matrix with the elevation,
azimuth and power values.
Figure 2.10(a) shows a 50x50 pixels image of a person on a chair with a toy gun concealed
under a T-shirt. As a reference, Fig. 2.10(b) shows an snapshot of the same scene recorded
with an infrared camera from a different point of view. The image has been acquired with
70 ms of integration time per pixel. The calibration has been performed applying the curve
given in Fig. 2.6 and using an absorber as a reference temperature. Even though the image
has been acquired in an indoor environment, still there is enough contrast between the toy
gun and the person to identify the shape of the object.
The total acquisition time is 5 min, yielding a mean acquisition time per pixel of 120 ms
taking into account the mechanical movement. The theoretical radiometric resolution of the
image is 0.22 K calculated from the measured value of ∆T in section 2.2.3. However, since
only one reference calibration is performed, the radiometric resolution is degraded by drifts
in the radiometer response.
A second example of an indoor image from a standing person carrying a toy gun on the
waist is shown in Fig. 2.11(b). It consists of a radiometric image with 100x40 pixels acquired in 7 minutes. The radiometric image has 19 K of dynamic range, showing an apparent
temperature of 295 K for the background and 305 K for the person. The toy gun and the belt
buckle are recognizable as well as the mobile phone carried on the pocket.
The apparent temperature of the person skin in the image will depend on the mean value
between its physical temperature and the reflected brightness temperature of the environment.
The metal surface of the gun however has a reflectivity value of r = 1, thus only reflecting
2.2 Total-power radiometer with mechanical beam-scanning
(a)
29
(b)
Figure 2.10: (a) W-band radiometric indoor image of a person on a chair with a concealed toy gun
under a T-shirt. (b) Infrared image of the same scene.
(a)
(b)
(c)
Figure 2.11: (a) Optical, (b) radiometric and (b) infrared indoor images of a standing person
with a concealed toy gun under a T-shirt.
the environmental brightness temperature. As a result of the low contrast of the scenario, a
noisy image is obtained and the gun is detected but hard to identify. An infrared image of the
imaged scene is presented in Fig. 2.11(c). Even though the spatial resolution of the infrared
image is greater than the radiometric image, the toy gun is harder to be detected since the
T-shirt is more opaque to infrared frequencies.
Fig. 2.12(b) presents a 100x50 pixels image of a person with a concealed toy gun as in
30
Chapter 2
Fig. 2.11(b), however in this case the image has been acquired in an outdoor environment.
The dynamic range of the image is around 200 K with a background apparent temperature
of approximately 100 K. The image has been obtained in a roof of a building with an tilted
metallic plate that reflects the sky as shown in Fig. 2.12(a). Therefore the background of
the image has the same brightness temperature as the sky. A temperature gradient of around
50 K is observed in the body. This effect is due to the incidence angle of the radiometer at the
person.
For a negative incidence angle, that is when aiming below the waist of the person, the body
is reflecting the floor of the roof that is around 310 K of physical temperature. Hence, this
part of the image appears warmer due to the contribution of the building and the surroundings.
For positive incidence angles the body reflects the sky reducing the apparent temperature of
this part of the body. Furthermore, for high incidence angles there is a distortion caused by
the projection of the beam on the body and by the displacement of the focus of the reflector.
This distortion is clearly observed in the image as a stretched neck. The toy gun appears with
an apparent temperature of around 240 K since it reflects partially the sky. The high contrast
of the image compared with the radiometer sensitivity provides a clean image compared with
the noisy image presented in Fig. 2.11(b).
The radiometer sensitivity is enough to detect a concealed toy gun under a T-shirt in an
indoor environment. However due to the low contrast of the image the identification of the
object is hard to achieve. In the outdoor environment, where the contrast is clearly higher
than the radiometric sensitivity the smooth edges and the clean image allows both detection
and identification of the concealed object. Appendix A shows a variety of outdoor images
obtained with the TPR radiometer described in this section. The images show the body shape
of each person in a way that is impossible to see from an optical image. Hence, mmW images
can be used as a source of biometric information.
2.3
Synthetic Aperture (SA) Interferometric Radiometry
Whereas the TPR radiometer is formed by just one receiver, the interferometric radiometer
is composed by multiple receivers forming an SA array. Each receiver element captures the
radiation coming from the scene, performs its demodulation and sends the processed signal
to a correlator processing unit. By correlating all combinations of signals coming from all
receiver pairs, the so-called visibility values of the scene are obtained, being related with
the temperature map of the scene by a Fourier Transform (FT). In the following sections,
the basic concepts of SA radiometry are introduced with special emphasis on performance
parameters such as radiometric sensitivity and spatial resolution.
2.3.1
Time-domain correlation
Figure 2.13 shows a block diagram of a basic passive interferometer composed by two radiometric receivers and a correlator. The process of capturing the thermal noise from the
scene is also depicted in the figure. Assuming that both receivers are equal, the result of the
2.3 Synthetic Aperture (SA) Interferometric Radiometry
31
(a)
(b)
Figure 2.12: (a) Optical and (b) radiometric infrared outdoor images of a standing person
with a concealed toy gun under a T-shirt.
Bandpass
filter
Antenna
r1
TB( ,f)
Amplifier
nr1(t)
ni1(t)
Integrator
1
2
H1(f)
nr1(t),n*r2(t)
r2
ni2(t)
H2(f)
nr2(t)
Figure 2.13: Reception of the scene thermal radiation by two receivers and their
block diagrams representing the correlation process.
correlation is
1
kB
hnr1 (t), n∗r2 (t)i =
2
Ωp
ZZ
4π
Z
∞
TB (θ, φ)t(θ, φ)kH(f )k2 e−jk(r2 −r1 ) df dΩ,
(2.20)
0
where H(f ) is the spectral response of the receiver chain consisting basically of the bandpass filter and the amplifier, the 21 term is considered since only the signal associated to one
polarization state is captured, t(θ, φ) is the normalized power pattern of the single element
antenna, k = 2π
λ is the wavenumber and Ωp is the antenna pattern solid angle. The term that
takes into account the decorrelation effects that appear when correlating band-limited signals
32
Chapter 2
1
0.8
r(t)
0.6
0.4
0.2
0
4
B
3
B
2
B
1
B
0
t [s]
1
B
2
B
3
B
4
B
Figure 2.14: Modulus of the fringe washing function ke
rk for ideal rectangular filtering with bandwidth B.
is the so-called fringe washing function re(t) and is defined as
re(t) =
e−j2πf0 t
BG
Z
0
∞
kH(f )k2 ej2πf t df,
(2.21)
where B is the noise equivalent bandwidth of the filter and G is the amplifier gain. Hence,
(2.20) can be rewritten as
ZZ
1
kB BG
∆r
∗
hnr1 (t), nr2 (t)i =
ejk0 ∆r dΩ,
(2.22)
TB (θ, φ)t(θ, φ)e
r
2
Ωp
c
4π
where k0 is the wavenumber associated with the central frequency of the filter and ∆r =
r2 − r1 . The result of the integral shown in (2.21) gives the following result for the temporal
definition of the fringe washing function for a rectangular filter with bandwidth B:
re(t) = e−j2πf0 t sinc(Bt).
(2.23)
1
Figure 2.14 shows a plot of (2.23) pointing out that ∆r
c B to maintain the correlation
between the signals of both receivers. Otherwise, the correlation level could fall below the
1
sensitivity of the receiver or even it can be canceled out if ∆r
c = B . In practice, this means
that the Field of View (FoV) is constrained by the bandwidth of the receiver. If a large
bandwidth is used to improve the sensitivity of the receiver, the FoV will be reduced and
viceversa.
2.3.2
Visibility function
A SA interferometric radiometer is formed by an array of antennas such as the one given
in Fig. 2.15 where the receiver elements are represented by black dots. It is convenient to
express the coordinate system in direction cosines ξ = sin θ cos φ and η = sin θ sin φ to simplify the formulation. Hence, the path difference ∆r of the signals captured by two receivers
can be approximated by ∆r ≈ −[ξ(x2 − x1 ) + η(y2 − y1 )] if the paraxial approximation
2.3 Synthetic Aperture (SA) Interferometric Radiometry
33
Figure 2.15: Geometry of a 2D-SA T-shape interferometric radiometer.
is assumed, where (xi , yi ) are the antenna coordinates. If the coordinates (u, v) are defined
1 y2 −y1
as the normalized antenna spacing (u, v) = ( x2 −x
λ ,
λ ), (2.22) can be expressed for any
pair of receivers as
ZZ
1
TB (ξ, η) − Tr
kB BG
uξ + vη
∗
p
hnri (t), nrj (t)i =
t(ξ, η)e
r −
e−j2π(uξ+vη) dξdη,
2
2
2
Ωp
f
0
1−ξ −η
ξ 2 +η 2 ≤1
(2.24)
where the receiver equivalent noise temperature Tr term is added to account for the coupling
between antennas [54]. The function containing the cross-power spectral density of the signals of all combinations of receiver pairs (i, j) is defined as the visibility function Vij (u, v)
and is given by
1
nri (t), n∗rj (t) ,
(2.25)
Vij (u, v) =
2kB BG
For identical receivers there is no distinction among visibilities corresponding to the same
baseline Vij (u, v) = V (u, v). In this case, from (2.24) and (2.25) the relationship between
the temperature map TB (ξ, η) of the scene and the visibility function is given by a FT [55]:
"
#
TB (ξ, η) − Tr
uξ + vη t(ξ, η)
V (u, v) = F p
re −
= F [TB0 (ξ, η)] [K],
(2.26)
f0
Ωp
1 − ξ2 − η2
where TB0 (ξ, η) is the modified brightness temperature of the scene including the antenna
pattern, the fringe washing function and the −Tr term.
Note from (2.26) that since the (u, v) space is sampled with discrete intervals (du, dv),
the angular dimensions of the target is constrained by the Nyquist theorem. If the FoV dimensions are given by (ξmax , ηmax ) the antenna separation in wavelength units is given by the
Nyquist sampling theorem (du = (2ξmax )−1 and dv = (2ηmax )−1 ). Note that if the antenna
34
Chapter 2
1
AF
0.5
0
−0.5
-2
umax
-3
4umax
-1
umax
-1
2umax
0
ξ
Synthetic aperture
Real aperture
1
1
3
2
2umax umax 4umax umax
Figure 2.16: Comparison between array factors of a SA and a rectangular RA.
separation (du and dv) is greater than λ0 /2 (where λ0 is the system wavelength at the central
frequency of the filter), the image presents aliasing of the scene background. However, this
issue can be solved in screener applications where differential imaging, with respect to an homogeneous background, can be used to set the alias zone to zero and cancel its contribution
to the reconstructed image [56].
2.3.3
Beamwidth of the synthesized beam
The number of measured visibility samples is limited and depends on the number of antennas.
Therefore the (u, v) domain is windowed with a window W (u, v) that extends to the array
size (umax , vmax )
ZZ
TB0 (ξ, η) =
W (u, v)V (u, v)ej2π(uξ+vη) dudv,
(2.27)
where the product W (u, v)V (u, v) in the transformed domain (u, v) is equivalent to a convolution in the (ξ, η) domain of their inverse Fourier transforms
ZZ
TB0 (ξ, η) =
TB0 (ξ 0 , η 0 )AF (ξ − ξ 0 , η − η 0 )dξ 0 dη 0 ,
(2.28)
where the inverse Fourier Transform (iFT) of the window is the antenna factor AF (ξ, η), also
called point source response [57] [58]. When a rectangular window is used to account for the
finite coverage of the (u, v) domain, the array factor is defined as
AF (ξ, η) = sinc(2umax ξ)sinc(2vmax η).
(2.29)
The Half-Power Beamwidth (HPBW) for both x and y axes is given by
0.60
∆θx ∼
= ∆ξ =
umax
;
0.60
∆θy ∼
.
= ∆η =
vmax
(2.30)
It must be pointed out that a physical aperture with uniform fields and the same size in the
sampling domain 2umax x2vmax would have a different HPBW. In this case, the normalized
2.3 Synthetic Aperture (SA) Interferometric Radiometry
35
antenna power pattern would be approximated for small θ values by [59]:
2
2
t(ξ, η) ∼
= [sinc(2umax ξ)] [sinc(2vmax η)] .
(2.31)
And, due to the squared terms, the HPBW of the equivalent aperture would be
0.44
∆θx ∼
=
umax
;
0.44
∆θy ∼
.
=
vmax
(2.32)
Figure 2.16 shows a comparison between antenna factors of a SA and a RA. For apertures
of the same size, the RA yields better spatial resolution than the SA.
2.3.4
Pixel overlapping in the synthesized images
Due to the Discrete Fourier Transform (DFT) properties, in the (ξ, η) domain the pixels are
equally spaced with a separation
dξ =
1
2umax
;
dη =
1
.
2vmax
(2.33)
In addition, the T-shaped array in Fig. 2.15 measures the visibility samples in a square of
Nu xNv equally spaced points in the (u, v) domain given by
Nu = 2
umax
+1
du
;
Nv = 2
vmax
+ 1.
dv
(2.34)
Hence, from (2.34) and (2.33), the number of pixels in the synthesized domain (ξ, η) equals
the number of visibility samples in the (u, v) domain:
2ξmax
+ 1 = Nu ;
dξ
2ηmax
=
+ 1 = Nv .
dη
Npx =
Npy
(2.35)
For a large number of antennas, pixel spacing can be given as a function of the synthesized
beam HPBW in each of the orthogonal directions by combining (2.30) into (2.33):
dξ =
∆ξ
1.2
;
dη =
∆η
.
1.2
(2.36)
It is shown that pixel separation is lower than the HPBW. Therefore, the interferometric
radiometer with rectangular taper yields to a pixel overlapping factor of 1.2. This factor will
be used when comparing the performances of the interferometer and the RA radiometer in
chapter 3.
2.3.5
Radiometric sensitivity
The variance at the output of the correlator and therefore the variance of a single visibility
measurement σv2 is given by [60]:
2
2
σv2 = ρr1 ρr2 + ρ2r1r2 = kB
(TA2 + Tsys
)B 2 ,
(2.37)
36
Chapter 2
4.5
RMS−TX
RMS−TY
4
∆ T [K]
3.5
3
2.5
2
1.5
−0.8
−0.6
−0.4
−0.2
0
η
0.2
0.4
0.6
0.8
Figure 2.17: Radiometric sensitivity of the MIRAS/SMOS instrument over the ocean compared
with the theoretical estimation as given in [62].
where ρri is the autocorrelation at the origin of the signal nri (t) and ρr1r2 is the crosscorrelation at the origin between nr1 (t) and nr2 (t). Hence, if TA Tsys , the temperature
standard deviation of a visibility measurement is
Tsys
∆Tv = √
Bτ
[K].
(2.38)
In order to calculate the standard deviation of the modified brightness temperature, the inversion equation (2.27) is discretized
XX
TB0 (ξ, η) = ∆s
W (umn , vmn )V (umn , vmn )ej2π(umn ξ+vmn η) ,
(2.39)
m
n
where ∆s is the elementary area in (ξ, η). Hence, if visibility errors are uncorrelated the
standard deviation of the modified brightness temperature is
s
XX
p
T
0
2 = ∆s √sys α
∆TB (ξ, η) = ∆s∆Tv
Wmn
Nv ,
(2.40)
w
Bτ
m n
where αw is a parameter that depends on the window and Nv is the number of visibility
samples. From (2.26) and (2.40), the radiometric resolution of a SA radiometer imaging an
extended source of thermal radiation is [61]:
αw αs p
TA + TR Ωp p
1 − ξ2 − η2
Nv [K]
(2.41)
∆TB (ξ, η) = ∆s √
αf
Bτ t(ξ, η)
where αs takes into account the sensitivity loss due to non-analog correlation and αf takes
into account the pre-detection filter shape.
The accuracy of this formula has been recently validated by the MIRAS/SMOS instrument [62] launched on November 2009. Figure 2.17 shows a comparison between the radiometric sensitivity ∆TB of the Microwave Imaging Radiometer using Aperture Synthesis (MIRAS) instrument calculated with (2.41) (dotted lines) and measured by means of
brightness temperature images over the ocean (continuous line) for both horizontal (Tx) and
vertical (Ty) polarizations at the antenna plane.
2.4 Conclusion
2.4
37
Conclusion
In this chapter, a brief description of classical radiometry concepts has been performed as
an introduction of the research presented in this document. Special attention is paid to SA
interferometric radiometry since the main research is done in this area.
In addition, a practical study of mmW radiometry has been presented in this chapter,
exposing the imaging capabilities of a mechanically scanned radiometer for concealing object
detection. The simplicity of the receiver architecture and its good performance in terms of
spatial resolution and radiometric sensitivity makes it appropriate for applications where the
acquisition time is not constrained. The antenna subsystem achieves enough spatial resolution
to detect objects with dimensions on the order of several centimeters. In addition, having
radiometric sensitivity close to 1 K has allowed the acquisition of low-contrast indoor images
that reveal concealed objects with only few degrees of temperature contrast.
Nevertheless, it is unfeasible to use a single-receiver mechanically scanned system for
real-time imaging purposes. The following chapters present performance studies and practical
solutions with the objective of optimizing the acquisition time and the cost of the imaging
system.
38
Chapter 2
C HAPTER 3
Millimeter-wave Performance Constraints
for Passive Close-Range Screening
I
N this chapter, a theoretical study of the performance constraints appearing in passive close-
range screening are studied. Three types of radiometers have been analyzed in terms of
radiometric sensitivity and spatial resolution: 1) the Two-Dimensional Synthetic Aperture
(2D-SA) radiometer; the One-Dimensional Synthetic Aperture (1D-SA) radiometer and the
Real-Aperture (RA) radiometer. The analytical expressions for the radiometric resolution, the
number of required antennas and the number of pixels in the image are derived taking into
account the distortion produced by the Near Field (NF) geometry at non-boresight directions
where the distortion is dominant. The image distortion caused by the NF geometry is assessed
by using 2D-SA screener simulations.
An screener geometry based on a sparse linear array is proposed as an optimum solution to
achieve the best performance with the minimum number of receivers. If a moving walkway is
used with a sparse linear array, no mechanical movements are needed on the receiver. Special
attention is paid to this system since it solves problems regarding the number of receivers and
acquisition time. Based on theoretical results a performance comparison among the studied
systems is carried out to show the advantages and drawbacks when using the radiometers in
a close-range screening application. Additionally the screener performance in a close-range
environment is discussed from the results obtained in the aforementioned comparison. 1
3.1
Close-range aperture synthesis
In this section the performance expressions for the 2D-SA, 1D-SA and RA radiometers are
particularized for close-range screening. In the case of the interferometer systems, a T-shape
array is the optimum configuration regarding a rectangular Field of View (FoV) as the one
required by screening systems [60]. Therefore, the analytical expressions of sensitivity and
1 The
following sections of this chapter may contain verbatim text and figures from [J2].
40
Chapter 3
Figure 3.1: Imaging setup used to compare different screening configurations.
spatial resolution are derived for this geometry. Figure 3.1 shows the screener geometry
and its disposition with respect the scene. The scene dimensions 2Wx2H together with the
imaging range r define the FoV of the system.
In order to use the inverse Fast Fourier Transform (iFFT) to obtain the image from the
visibilities measured by the interferometric radiometer the targets of interest should be located
in the Far Field (FF) range of the array [63]. For close-range operation, a Near-to-Far-Field
correction is proposed in [64] [65] to use the Fast Fourier Transform (FFT) to retrieve images
acquired in NF range if a certain degree of distortion at the edges of the FoV is allowed. It
is considered that the scene is in the NF of the array if the distance between the array and
the scene is r < 2Da2 /λ, where Da is the array physical size. The equality is given when
the maximum phase error due to the paraxial approximation is π/8. In this situation, the
phase error present in the visibilities should be compensated in order to avoid distortion if an
NF
iFFT is used as an image focusing technique. From the measured visibilities in NF Vkj
, an
estimation of the FF visibilities is given by
FF
NF −jk0 (rk −rj ) −j2π(uξ+vη)
Vbkj
= Vkj
e
e
.
(3.1)
The correction consists of a phase compensation introduced by the term e−jk0 (rk −rj ) , where
ri is the distance from the antenna “i” to the center pixel of the image. Hence, by using this
correction, the center pixel is properly focused whereas the focusing level is decreased as
the pixels are further from the center. Note that the target is in the FF of any single antenna
3.1 Close-range aperture synthesis
41
element in the array and close-range distortion is exclusively caused by non-paraxial imaging
and by the projection of the screener beams on the image plane.
The following points apply the formulation for 2D-SA, 1D-SA and RA radiometers developed in [64] to close-range applications. The general sensitivity equations for the different
radiometers are elaborated for a NF geometry. These expressions can be directly compared
at an equivalent imaging time (ts ) depending on the system bandwidth, system temperature,
scene range and dimensions and required resolution. In order to analyze several radiometer
configurations, only boresight radiometric resolution is taken into account.
3.1.1
Single element constraints
Equation (2.41) shows that boresight radiometric resolution is improved by minimizing the
single element solid angle Ωe . However, since off-boresight radiometric resolution is degraded with the antenna pattern, a tradeoff is achieved by constraining this degradation to a
maximum factor of 2 when the single element Half-Power Beamwidth (HPBW) matches the
FoV. To assess the feasibility of this approach we must notice that the maximum size of a
single element in the array is limited by the minimum antenna separation du and dv. In this
case, according to (2.32), the single element HPBW for an aperture with uniform fields and
size du · dv is given by
0.88
0.88
= 0.88(2ξmax ) ; ∆θey =
= 0.88(2ηmax ).
(3.2)
du
dv
Therefore, in the case of practical antennas the HPBW of the single element antenna can be
adapted to the scene FoV by using an aperture slightly smaller than the minimum antenna
separation as described by the following expression:
∆θex =
Lx ∼
= 0.88du
Ly ∼
= 0.88dv
(3.3)
where Lx and Ly are the aperture dimensions of the single element antenna normalized to the
system wavelength.
3.1.2
Particularized radiometric sensitivity
For the sake of simplicity, rectangular tapering, analog correlation and ideal rectangular predetection filtering are considered in (2.41) yielding
p
TA + TR
∆TB = √
du · dv · Ωe Nu Nv ,
(3.4)
Bts
where the elemental sampling area given by ∆s = du·dv has been considered for rectangular
sampling. It should be pointed out that according to (3.4) ∆TB is optimized if the single
element solid angle Ωe is minimized by matching the HPBW of the single element antenna
pattern to the FoV.
In the case of a large number of elements in the array, from (2.30) and (2.34) the following
equation is obtained
4umax vmax ∼ 1 4 · 0.602
du · dv ∼
.
=
=
Nu Nv
Nu Nv ∆θx ∆θy
(3.5)
42
Chapter 3
Now, if the synthesized solid angle is approximated by the product of the HPBW in the two
orthogonal directions, Ωsyn ∼
= ∆θx ∆θy , and taking into account the relationship between
solid angle and effective area (Ωsyn /Ωe = Ae /Asyn ) the following expression is obtained
TA + TR Asyn
1
√
∆TB = 0.72 √
,
Bts Ae
Nmu Nmv
(3.6)
where Asyn and Ae are the effective areas of the synthetic aperture and the single element
aperture. Note that (3.6) is consistent with the approximate expression usually found in the
literature [66], where the number of measured visibility samples Nmu · Nmv = Nu · Nv /4 is
used (the Hermitian visibility samples are not taken into account).
3.1.3
2D synthetic aperture interferometric radiometer
In order to obtain the NF sensitivity expression, (3.4) is transformed using the following
parameters:
• Boresight spatial resolution in x: ∆x = r∆θx ∼
= r∆ξ
• Boresight spatial resolution in y: ∆y = r∆θy ∼
= r∆η
• Target size along x: 2ξmax = 2 sin(arctan( W
r ))
• Target size along y: 2ηmax = 2 sin(arctan( Hr ))
Since the synthesized image is computed as the FFT of the visibility samples, if Fourier
interpolation is not used, the number of independent pixels in the synthesized image (Npx and
Npy ) is coincident with the number of visibility samples (Nvx and Nvy ). In order to take into
account the smearing of the image, the relation between the Effective Field of View (EFoV)
and the Instantaneous Field of View (IFoV) is considered for the computation of the number
of pixels.
The angular resolution (∆θx and ∆θy ) is approximated by the increment of the direction
cosines (∆ξ and ∆η) at boresight. If the single element HPBW matches the FoV: Ωe ∼
=
∆θex ∆θey ∼
= 2ξmax 2ηmax and Ωe ∆s = 1. Thus if the NF distortion can be neglected ∆TB
is independent on the imaging range as presented in point 3.1.6 and depends on the receiver
parameters, the scene dimensions and the spatial resolution. Furthermore, as the antenna
separation is also adapted to the FoV, the spatial resolution for a given number of antennas
is approximately maintained independent of the range. Due to the pixel overlapping of the
synthesized images given as a result of (2.35) and (2.36), the number of pixels related with
the FoV and the spatial resolution is
2ξmax
2ξmax
+ 1 ≈ 1.2
;
∆θx
∆θx
2ηmax
2ηmax
= 1.2
+ 1 ≈ 1.2
.
∆θy
∆θy
Nu = Npx = 1.2
(3.7)
Nv = Npy
(3.8)
3.1 Close-range aperture synthesis
43
By substituting the aforementioned parameters in (3.4) the resulting expression is
NF
∆T2D
3.1.4
H
arctan( W
Tsys
r ) arctan( r )
= 2.4 √
H
Bts sin(arctan( W
r )) sin(arctan( r ))
s
H
sin(arctan( W
r )) sin(arctan( r ))
∆x
r
∆y
r
.
(3.9)
1D synthetic aperture interferometric radiometer
A 1D-SA radiometer that performs synthetic imaging in the vertical direction y and real
aperture in horizontal direction x is studied. The 1D-SA radiometer must acquire a vertical
line of pixels in ti = ts /Npx seconds in order to have a 2D image in ts seconds. In this case,
the radiometric resolution is approximated by the following expression
∆TB =
p
TA + TR
√
∆θy dv Nv Npx .
Bts
(3.10)
The following equation is obtained if the parameters of (3.10) are transformed to consider the
NF geometry
NF
∆T1D
=
√
arctan( Hr )
Tsys
4.8 √
Bts sin(arctan( Hr ))
s
H
arctan( W
r ) sin(arctan( r ))
∆x
r
∆y
r
r
EFOV
.
IFOV
(3.11)
As in the 2D-SA case, the single element HPBW must match the FoV and the antenna separation dv is adjusted to the image FoV (dv = (2ηmax )−1 ). The number of mechanically
scanned pixels depends on the scene distance for close-range imaging resulting in
Npx =
3.1.5
2 arctan ( W
r ) EFOV
.
∆x
IFOV
r
(3.12)
Real aperture radiometer
A system based on a single receiver radiometer with a beam-scanning antenna system has
been considered for the RA screener configuration. In this case if Npx · Npy pixels are imaged
in ts seconds, the integration time for each pixel ti must be reduced accordingly, yielding a
radiometric sensitivity
TA + TR p
Npx Npy .
(3.13)
∆TB = √
Bts
Taking into account the number of pixels in NF, (3.13) develops into
NF
∆TRA
Tsys
=√
Bts
s
H
2 arctan( W
r ) 2 arctan( r ) EFOV
.
∆x
∆y
IFOV
r
r
(3.14)
44
3.1.6
Chapter 3
Far field radiometric sensitivity
In the FF screening range (r W, H), the trigonometric functions of (3.9), (3.11) and (3.14)
can be approximated by the angles, yielding the following expression
s
TA + TR 2W 2H EFOV
FF
∆TB = √
.
(3.15)
∆x ∆y IFOV
Bts
Hence, the radiometric sensitivity ∆TB in the FF range tends to the same value for the three
studied systems. Note that the Interferometric Radiometer Uncertainty Principle derived in
[61] can be translated to the screener case by the following expression
∆TB · ∆x ·
√
Tsys EFOV √
2 W H.
ts = √
B IFOV
(3.16)
The performance parameters have been grouped in the left hand side of the equation whereas
the system parameters are in the right hand side. A clear tradeoff between spatial resolution
and radiometric sensitivity is shown in the expression.
3.2
Screener design parameters
In the following sections the expressions derived in section 3.1 are compared depending on
several parameters. Additionally, a sparse array configuration is described for the 1D-SA
radiometer. It should be pointed out that time delays caused by mechanical movements have
been neglected in the comparison.
3.2.1
Radiometric sensitivity comparison
The radiometric sensitivity ∆TB describes the capacity of the radiometer to distinguish among
small scene contrasts in the image and hence, the capacity of detecting concealed objects with
an apparent temperature similar to the background. The three radiometer systems are compared with similar front-end characteristics: TR = 300 K (3 dB noise figure), TA = 300 K,
B = 500 MHz, ∆x = ∆y = 3 cm, and a target size 2H = 180 cm and 2W = 90 cm
(Fig.3.1). A relation between EFoV and IFoV is chosen as EFoV = 1.2IFoV for mechanical
scanning to compare all systems in equal smearing conditions. These parameters will be used
in the following points to compare the different radiometer architectures unless otherwise
noted.
Figure 3.2(a) shows the variation of ∆TB with the imaging time calculated with (3.9),
(3.11) and (3.14) at a range r = 1.25 m. In this particular case, ξmax = 0.33 and ηmax = 0.58
yielding an antenna separation of du = 1.51 and dv = 0.86. The spatial resolution sets
umax = vmax = 25 and the number of pixels Nu = 34 and Nv = 59. The result is
similar for the three radiometers and shows that with the studied system configuration the
radiometric sensitivity is below 1.5 K for an image acquisition time of 1 s at a bandwidth
of 500 MHz. Sub-second imaging or improved radiometric sensitivity requires larger predetection bandwidth (e.g. B = 2 GHz).
3.2 Screener design parameters
45
6
B=500 MHz
1.4
1.3
∆ T [K]
∆ T [K]
4
1.5
2D-SA
1D-SA
RA
5
3
2
2D−SA
1D−SA
RA
1.1
1
0
1.2
1
B=2 GHz
0
0.2
0.4
0.6
0.8
0.9
0.5
1
ts [s]
1
1.5
(a)
3.5
4
80
70
60
50
40
Antennas
Npx: 2D−SA
Npy: 2D−SA
Npx: 1D−SA
Npy: 1D−SA
Npx: RA
Npy: RA
60
Pixels
3
(b)
80
2D−SA
1D−SA
RA
40
20
30
20
0.5
2
2.5
Range [m]
1
1.5
2
2.5
Range [m]
(c)
3
3.5
4
0
1.5
1
1.5
2
2.5
Range [m]
3
3.5
4
(d)
Figure 3.2: (a) Radiometric sensitivity against integration time and bandwidth of the radiometers. Subsecond imaging and sub-Kelvin sensitivity requires a large bandwidth. (b) Radiometric sensitivity depending on the scene distance from the radiometer. (c) Number of pixels in the image for the different
studied radiometers. (d) Number of antennas required to fulfill the FoV and spatial resolution specifications depending on the scene range.
The range dependance of the radiometric sensitivity in passive NF imaging is pointed out
in Fig. 3.2(b). For the aforementioned system characteristics and for a range between 0.5
and 2 meters the sensitivity is dependent on the range. For a range larger than 2 meters the
sensitivity tends to a value of 1.4 K, close to the FF value. The variation of the sensitivity
in the NF range is due to the reduction of the number of pixels needed to acquire the image
as presented in Fig. 3.2(c). This effect occurs since the projection of the beam on the scene
degrades the spatial resolution at the edges and therefore the number of pixels required to
fill the scene is reduced. Furthermore, as the number of pixels is reduced, the number of
antennas is as well reduced in the case of the interferometric radiometers as shown in Fig.
3.2(d). Further discussion of NF distortion effects are carried out is section 3.3.2.
Table 3.1 shows a comparison made according to a similar front-end configuration at
1.25 m range with 3 cm of spatial resolution. The RA screener needs one receiver antenna
with an area of approximately 177 cm2 to obtain the desired spatial resolution whilst the
1D filled (*) interferometric array is composed by 31 antennas of 3.4 cm2 and the 2D array
contains 65 antennas with an area of 0.13 cm2 . The parameters specified for a 1D (**) array
represent the performance of an array thinned to 10 antennas. The compared systems have
nearly the same radiometric sensitivity if they are optimized for a specific range as shown in
Table 3.1.
46
Chapter 3
∆TB [ K]
1.26
1.31
1.31
1.33
RA
1D (*)
1D (**)
2D
Npx
35
35
35
35
Npy
64
60
60
60
Nvx
0
0
0
35
Nvy
0
60
60
60
Nant
1
31
10
65
Ae ( cm2 )
176.83
3.40
3.40
0.13
(*) Filled array. In this case the baselines are highly redundant.
(**) Thinned array. In this case the 1D-SA array has been thinned to 10 antennas.
Table 3.1: Screener comparison for similar front-end configuration
r = 1.25 m, ∆x = 3 cm, B = 500 MHz, ts = 1 s, Tsys = 600 K
Figure 3.3: Schematic of the antenna disposition in a sparse array composed of
10 antennas that synthesizes 37 visibilities (umax = 36du) [67].
20
∆T [K]
3
2D−SA
1D−SA
RA
1D−SA Sparse
2
10
5
1
0
15
∆y [cm]
4
0
5
10
15
20
25
30
0
35
N ant
Figure 3.4: Comparison depending on the number of antennas Nant of the radiometric sensitivity ∆T
and spatial resolution along the y-axis ∆y of the 2D-SA, 1D-SA, RA and 1D-SA sparse radiometers.
The calculation has been performed with the following system parameters: ts = 1, ∆x = 3 cm,
B = 500 MHz, H = 90 cm, W = 45 cm. r = 125 cm and Tsys = 600 K.
3.2.2
1D-SA sparse array
The main advantage of the 1D-SA is that the redundancy in the visibilities is greatly reduced
by using a thinned array with a minimum redundancy as described in [67]. In order to make
a comparison with the T-shape array, the number of antennas in each of the arms of a 2D-SA
sensor (Fig. 2.15) can be directly related to the number of visibility samples Nvx · Nvy used
to synthesize an image
Nax = Nvx
;
Nay =
1
(Nvy − 1).
2
(3.17)
If a 1D-SA sparse array is used to synthesize the image in the y direction, the larger baseline needed to have the same number of visibility samples (pixels) as in the T-shape case is
3.2 Screener design parameters
Sensor type
2D-SA T-shape
1D-SA sparse
47
∆y ∼
= 3 cm
66
10
∆y ∼
= 2 cm
99
12
∆y ∼
= 1 cm
197
17
Table 3.2: Number of antennas for a given boresight spatial resolution
Target size: 2H = 180 cm, 2W = 90 cm at r = 125 cm
Figure 3.5: Proposed imaging setup based on a 1D-SA radiometer. The vertical pixels are synthesized by the radiometers whereas the horizontal are obtained by translating the scenario using a moving
walkway.
vmax = 0.5(Nvy + 1), which gives the number of required antennas in the thinned array [19].
As an example, Fig. 3.3 shows the antenna arrangement of the sparse array with 10 antennas
where, in order to minimize the effect of NF distortion, the thinned array with better symmetry has been selected. A comparison of the spatial resolution ∆y and radiometric sensitivity
∆T among the studied radiometers is shown in Fig. 3.4 depending on the number of antennas
Nant . It is shown that the one-dimensional sparse array has an improved spatial resolution
with respect the 2D-SA and the 1D-SA for the same Nant . Nevertheless, the radiometric sensitivity is reduced for equivalent number of antennas. Table 3.2 gives the number of antennas
required in the two cases to yield the same spatial resolution in the synthesized direction. As
spatial resolution gets more stringent 1D-SA thinned arrays lead to a drastic reduction of the
number of antennas with relation to a 2D-SA sensor.
3.2.3
1D-SA screener with moving walkway
A screener system based on a 1D interferometric radiometer is proposed working at 94 GHz
consisting of a vertical thinned linear array of 10 antennas as the one explained in section
3.2.2. The radiometer array is used as a static imaging sensor whereas a moving walkway
translates the person in the horizontal direction. In this case, no moving mechanical parts
48
Chapter 3
RA
1D-SA
2D-SA
A DVANTAGES
D RAWBACKS
Use of direct detection receivers
No degradation of ∆T at the image edges
Requires mechanical scanning
Large single element antenna
Simple signal processing
Aiming problems in non-stable environments
1D images obtained in single acquisition
IF processing of large bandwidth signals
Thinned arrays can be used
Visibility redundancy can be minimized
1-D mechanical movement needed
Heterodyne receivers
A 2D image obtained in a single acquisition
∆T improved by averaging redundancy
IF processing of a large amount of correlations
Large number of receivers required
No mechanical movement needed
Heterodyne receivers
Table 3.3: Advantages and drawbacks of the radiometer configurations for close-range screening
purposes
in the screener are needed, reducing the design dimensions and cost. Figure 3.5 shows the
imaging setup describing the main geometrical parameters. A distance between the imaging
sensor and the scene has been chosen to be 1.25 m as a tradeoff in order to avoid the pixel
distortion on the edges (∆xmax = 1.22∆x) but still maintaining a small array (100 mm
length). If the speed of the moving walkway is fixed to 0.5 m/s, the required time to acquire
an image is fixed to 1.8 seconds. In this case, if a receiver with a Tsys = 600 K and a predetection bandwidth of 500 MHz is considered, the resulting ∆T from (3.11) is 1.4 K. The
angular resolution is obtained from (2.30) giving ∆θy = 0.96 ◦ at boresight (∆y = 2 cm).
In this proposed system, additional focusing in the horizontal axis is needed to provide
the required angular resolution in this direction. This can be achieved by using a cylindrical
λ
reflector with an aperture dimension of D = 1.2 ∆θ
= 220 cm.
x
3.3
Screener performance
Table 3.1 summarizes the performance of the different sensor configurations described so far
in order to show the feasibility of close-range radiometric screening with relatively small antenna size and reasonable receiver characteristics. Since the most suitable configuration will
depend, to a large extent, on the application and the environment, the following sections are
devoted to highlight the limitations and improvement paths in the case of synthetic apertures.
Additionally, Table 3.3 summarizes the advantages and drawbacks of each radiometer system
when used in a screener system.
3.3.1
Spatial/Radiometric resolution tradeoff
The tradeoff between the spatial and the radiometric resolutions when assessing the object detection capabilities of a passive screener system is described in this section. The temperature
contrasts in a certain beam projection on the scene are averaged. Therefore, an object with
smaller dimensions than the spatial resolution can be detected if the averaged pixel temperature differs with the contiguous pixels with a value greater than the radiometric sensitivity.
3.3 Screener performance
49
Figure 3.6: Schematic depicting the tradeoff between the spatial resolution and radiometric sensitivity
in the object detection problem for an ideal reflective target.
Nevertheless, it should be pointed out that two objects separated with a distance less than the
spatial resolution will be detected only as a one object.
Figure 3.6 shows a simplified schematic example of a scene consisting on a person at
a physical temperature of 37 ◦ C in front of a background being at 22 ◦ C (considering that
both have an emissivity of 1). Two metallic objects with different dimensions are placed
on the person reflecting the background temperature. A differential passive imaging system
with a spatial resolution of 3 cm detects the 1x3 cm object as a 3x3 cm spot with an apparent
temperature of 5 K below the body temperature. In the case of the 1x1 cm object, it is detected
as a 3x3 cm spot at 1.7 K below the body temperature.
Hence, an object with smaller dimensions than the spatial resolution of the system can be
detected if the radiometric sensitivity level is below the value given by
∆TB < (Tbody − Tbk )
Dx · Dy
,
∆x · ∆y
(3.18)
where DxxDy are the object dimensions. Note that for equal spatial resolution on the two
dimensions, the radiometric sensitivity requirement is inversely proportional to ∆x2 and gets
dramatically stringent at sub-centimetric resolution.
3.3.2
Off-axis performance degradation
Synthetic Aperture (SA) interferometric radiometers have two sources of NF distortion: 1)
the beam projection on the image plane; and 2) the paraxial approximation assumed when
reconstructing the temperature image from the visibilities applying an iFFT.
The first source of distortion produces a degradation of the spatial resolution at the edges
∆xmax with relation to the boresight value ∆x0 given by
∆xmax
1
=
2
∆x0
cos (arctan ( W
r ))
(3.19)
as a function of the range and target size (Fig. 3.7(a)). For distances below 2 m the spatial
resolution at the edges is deteriorated in the x- and y-axes. This effect causes a blurring
50
Chapter 3
2
1.5
y axis
x axis
1.3
1.2
1.6
1.4
1.1
1
0.5
2D−SA
1D−SA
RA
1.8
∆ T [K]
∆ x max /∆ x 0
1.4
1
1.5
2
Range [m]
2.5
3
1.2
−0.8
−0.6
−0.4
(a)
−0.2
0
y [m]
0.2
0.4
0.6
0.8
(b)
Figure 3.7: (a) Spatial resolution degradation at the edge of the FoV due to NF distortion. (b) Variation
of the radiometric resolution ∆TB along y-axis of the image for the three screener configurations. The
curves have been calculated with (2.41) and (3.14).
Beam Projection Distortion
(a)
(b)
Figure 3.8: 2D Screener simulation at f0 = 94 GHz and r = 0.6 m applying the NF to FF correction.
Decorrelation effects are neglected. (a) Scene with a 90x180 cm2 target consisting on an person with
metallic objects of the following dimensions: 1) 4x10 cm2 in the chest; 2) an L-shape object with 5 cm
width in the waist and 3) 3x5 cm2 in the ankle. The person has a differential temperature of 15 K with
respect the background. (b) Reconstructed image showing the effect of the beam projection distortion at
the edges.
of the image at the edges. Nevertheless, in a typical imaging scenario, the information is
concentrated at the center of the scene, and some distortion of the pixels at the borders of
the image can be allowed. Moreover, in the case of the interferometric radiometers the ∆TB
is also decreased in the edges as shown in Fig. 3.7(b). The dependence of ∆TB with the
pixel position is also shown in Fig. 2.17. Note that in the case of the RA radiometer, the
radiometric sensitivity does not vary along the axis. The conjunction of these two distortion
3.3 Screener performance
51
Corrected NF to FF / ∆x=5cm
0.8
0.6
0.6
0.4
0.4
0.2
0.2
y [m]
y [m]
NF / ∆x=5cm
0.8
0
−0.2
−0.4
−0.4
−0.6
−0.6
0 0.2
x [m]
0.4
5
−0.4 −0.2
(a)
0 0.2
x [m]
0.4
0
(b)
Corrected NF to FF / ∆x=4cm
NF / ∆x=3cm
Corrected NF to FF / ∆x=3cm
0.8
0.8
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0
0
y [m]
0.8
y [m]
0.8
y [m]
y [m]
10
−0.8
−0.4 −0.2
NF / ∆x=4cm
15
0
−0.2
−0.8
[K]
0
−0.2
−0.2
−0.2
−0.4
−0.4
−0.4
−0.4
−0.6
−0.6
−0.6
−0.6
−0.8
−0.4 −0.2
0 0.2
x [m]
(d)
0.4
−0.8
−0.4 −0.2
(e)
0 0.2
x [m]
0.4
15
10
0
−0.2
−0.8
[K]
5
−0.8
−0.4 −0.2
0 0.2
x [m]
(f)
0.4
−0.4 −0.2
0 0.2
x [m]
0.4
0
(g)
[K]
15
10
5
0
(i)
(j)
(k)
(l)
Figure 3.9: 2D Screener simulations of the scene shown in Fig. 3.8(a) with r = 1.2 m. Decorrelation effects are neglected. (a) Scene consisting on an person with metallic objects of the following dimensions: 1) 4x10 cm2 in the chest; 2) an L-shape object with 5 cm width in the waist and 3)
3x5 cm2 in the ankle. The person has a differential temperature of 15 K with respect the background.
Figures (a)(d)(f) (i)(k) are retrieved differential images using standard iFFT with a boresight HPBW
∆x = ∆y = {5, 4, 3, 2, 1} cm respectively. The objects 1) and 3) cannot be detected due to NF
distortion. Figures (b)(e)(g)(j)(l) are retrieved images after NF to FF correction with a boresight HPBW
∆x = ∆y = {5, 4, 3, 2, 1} cm respectively.
52
Chapter 3
B=10GHz / ∆x=3cm / f0 =94GHz
B=20GHz / ∆x=2cm / f0 =94GHz
B=10GHz / ∆x=2cm / f0 =94GHz
0.8
0.8
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0
0
y [m]
0.8
y [m]
0.8
y [m]
y [m]
B=20GHz / ∆x=3cm / f0 =94GHz
0
0
−0.2
−0.2
−0.2
−0.4
−0.4
−0.4
−0.4
−0.6
−0.6
−0.6
−0.6
−0.8
−0.8
−0.8
0 0.2
x [m]
0.4
−0.4 −0.2
(a)
0.4
0 0.2
x [m]
0.4
−0.4 −0.2
(c)
B=10GHz / ∆x=1cm / f0 =94GHz
B=20GHz / ∆x=3cm / f0 =35GHz
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
y [m]
0.6
y [m]
0.8
y [m]
0.8
0
−0.2
−0.2
−0.2
−0.4
−0.4
−0.4
−0.4
−0.6
−0.6
−0.6
−0.6
−0.8
−0.4 −0.2
0 0.2
x [m]
0.4
−0.8
−0.4 −0.2
0 0.2
x [m]
0.4
−0.8
−0.4 −0.2
0 0.2
x [m]
0.4
−0.4 −0.2
0 0.2
x [m]
0.4
(i)
B=20GHz / ∆x=2cm / f0 =35GHz
B=10GHz / ∆x=2cm / f0 =35GHz
B=20GHz / ∆x=1cm / f0 =35GHz
B=10GHz / ∆x=1cm / f0 =35GHz
0.8
0.8
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
y [m]
0.8
y [m]
0.8
y [m]
y [m]
(h)
0
−0.2
−0.2
−0.2
−0.4
−0.4
−0.4
−0.4
−0.6
−0.6
−0.6
−0.6
−0.8
−0.8
−0.8
0 0.2
x [m]
(k)
0.4
−0.4 −0.2
0 0.2
x [m]
(l)
0.4
0
[K]
15
10
0
−0.2
−0.4 −0.2
15
5
(g)
0
[K]
10
(f)
0
0
0
−0.2
−0.8
0.4
B=10GHz / ∆x=3cm / f0 =35GHz
0.8
0
0 0.2
x [m]
(d)
0.8
0
5
−0.8
−0.4 −0.2
(b)
B=20GHz / ∆x=1cm / f0 =94GHz
y [m]
0 0.2
x [m]
15
10
−0.2
−0.4 −0.2
[K]
5
−0.8
−0.4 −0.2
0 0.2
x [m]
(m)
0.4
−0.4 −0.2
0 0.2
x [m]
0.4
(n)
Figure 3.10: 2D Screener simulations of the scene shown in Fig. 3.8(a) with r = 1.2 m. Decorrelation
effects are taken into account. The simulations have been performed at two center frequencies f0 =
{94, 35} GHz and two RF bandwidths B = {10, 20} GHz. The differential images reconstructed at
f0 = 94 GHz are: (a)(c)(f) with B = 20 GHz and ∆x = ∆y = {3, 2, 1} cm respectively; (b)(d)(g)
with B = 10 GHz and ∆x = ∆y = {3, 2, 1} cm respectively. The results at f0 = 35 GHz are:
(h)(k)(m) with B = 20 GHz and ∆x = ∆y = {3, 2, 1} cm respectively;(i)(l)(n) with B = 10 GHz
and ∆x = ∆y = {3, 2, 1} cm respectively.
0
3.3 Screener performance
53
effects produced by the beam projection on the image plane reduces the detection capability
of the system at the edges. Figure 3.8(b) shows the distortion produced by the beam projection
on a reconstructed image at r = 0.6 m, where the NF to FF correction has been applied. The
edges of the image are affected by a blurring caused by a increment of the pixel dimension.
The object placed in the ankle cannot be detected due to the distortion. In the case that this
distortion level is unacceptable for the screener application, the radiometer should be placed
at a further range, thus implying an increment of size of the imaging array.
The second source of distortion is the assumption of the paraxial approximation in the
reconstruction of the image. This assumption produces a phase error when imaging at closerange that should be corrected to properly reconstruct the image [64] [65]. Figure 3.9 is
devoted to better illustrate the distortion effects produced in the close-range imaging. The
effect predominating in the images appearing in the figure is the one produced by the paraxial
approximation. An scenario with dimensions 2W = 90 cm and 2H = 180 cm has been
used as a reference target to foresee the distortion produced by using standard interferometric
techniques in the NF range. The scene contains a person at a differential temperature of 15 K
with respect the background. The person carries 3 metallic objects with different dimensions:
1) 4x10 cm2 in the chest; 2) an L-shape object with 5 cm width in the waist and 3) 3x5 cm2
in the ankle. Figures 3.9(a)(d)(f) (i)(k) are retrieved differential images using standard iFFT
with a boresight HPBW ∆x = ∆y = {5, 4, 3, 2, 1} cm respectively. It can be appreciated
that, as the spatial resolution is improved, the distortion is aggravated. This is due to the array
enlargement needed to achieve the required resolution. Hence, if the array is larger, the phase
error related to the paraxial approximation is increased. The phase error produces a distorted
image not suitable for identification of concealed objects.
Figures 3.9(b)(e)(g)(j)(l) are retrieved images after NF to FF correction with a boresight
HPBW ∆x = ∆y = {5, 4, 3, 2, 1} cm respectively. The reconstructed images after NF to
FF shows a reduced level of distortion an are suitable to detect the objects, nevertheless the
distortion level is increased at the edges as the spatial resolution is improved. The distortion
correction capabilities are reduced when the array dimensions are increased to improve the
spatial resolution. Hence, the Fig. 3.9(g) shows less distortion than 3.9(l). The results presented in Fig. 3.9 also show the detection capabilities depending on the spatial resolution. In
Fig. 3.9(b), with ∆x = ∆y = 5 cm the object concealed in the ankle cannot be detected due
to a lack of spatial resolution. However, in Fig. 3.9(l) the object is clearly identified.
3.3.3
Decorrelation effects
Section 3.3.4 will show that a large predetection bandwidth B is required to significantly
improve the performance of the screener with relation to the example described in Table
3.1. However, although analog correlation allows very large bandwidth, decorrelation may
degrade off-axis spatial resolution. Simulation of the NF visibilities in Fig. 3.10 has included
the impact of decorrelation when an ideal rectangular bandpass filter in each receiver is taken
into account. In this case, the fringe washing function for the baseline (u, v) given by a pair
of receivers “k”and “j” has been modeled as:
B
(rk − rj )
(3.20)
rkj (τd ) = sinc
c0
54
Chapter 3
where the delay τd between the radiation collected by antennas k and j is direction dependent, c0 = 3 · 108 m/ s and rk,j the distance of each pixel in the image to antennas
k and j respectively. Figure 3.10 shows the impact of decorrelation effects in the reconstructed image for all combinations of f0 = {94, 35} GHz, ∆x = ∆y = {3, 2, 1} cm and
B = {10, 20} GHz. For f0 = 94 GHz, the impact of decorrelation is negligible for predetection bandwidths of B = 10 GHz. However, the effects are noticeable for B = 20 GHz,
mainly if ∆x = ∆y = 1 cm. For f0 = 35 GHz, the decorrelation effects seriously impact
the image, hindering the detection of objects at the edges of the image.At lower frequency
bands the decorrelation impact of pre-detection bandwidth is higher due to the larger size of
the array. This result justify that in order to avoid the NF distortion in the image MillimeterWave (mmW) frequency bands should be selected for close-range imaging.
3.3.4
Improved performance
The results presented in Table 3.1 and Fig. 3.9 are related to a quite simple sensor design
to show, as a first approach, the main performance parameters of a close-range screener.
However, the enhanced performance that some applications may require can be achieved on
penalty of higher cost and complexity. The improvement of any of the performance parameters of (3.16), while keeping constant the others, can only be achieved by improving the
system parameters in the right hand side of the equation:
• System temperature. Since the antenna temperature is fixed to TA ∼
= 300 K, system
temperature can only be significantly improved if a cryogenic front end, either passive
or active, is foreseen to reduce
TR = 300 K. The theoretical maximum improvement
√
factor in the ∆TB · ∆x · ts product is 2 when TR = 0 K.
• Predetection bandwidth. B can be greatly increased if analog correlation, IF channelization or a combination of both is taken into account. The simulation in the previous
section has shown that very large predetection bandwidths are feasible with negligible
decorrelation effects in the W-band. If an effective bandwidth B = 10 GHz is used the
sensor parameters would be improved by a factor of 4.5 with respect the curves shown
in section 3.2.1.
• Redundancy. The radiometric resolution expressions given in [61] and [66] do not take
into account any level of redundancy. Two baselines are said to be redundant one with
the other when the distance and the direction of the two receivers involved in each one
of the two baselines are the same. Unfortunately, the level of redundancy in 2D arrays
is marginal (only in the direction of the axis). On the other hand, 1D-AS arrays have a
large degree of redundancy but can be thinned to a large extent to minimize the number
of antennas. Therefore, the most direct way to reduce radiometric noise by averaging
simultaneous independent measurements is by replicating the whole sensor. This is
particularly efficient in the case of 1D-SA sparse array.
For instance in Table 3.1 2D-SA and 1D-SA sparse sensors require 65 and 10 antennas
respectively to achieve the same radiometric resolution (∆TB = 1.3 K). If 6 1D-SA
sparse arrays are placed together pointing to the same pixel (or adjacent pixels in √
the
mechanically scanned direction), radiometric resolution is improved by a factor 6
with relation to the 2D case.
3.4 Conclusion
55
• Environment. The absorbers placed in front of the FoV can be cooled down to increase the contrast between reflective targets and the body temperature. For instance,
surrounding temperature Tph = 12 ◦ C increases the contrast from 15 K to 25 K and
relaxes ∆TB requirement by a factor 1.7.
3.4
Conclusion
The theoretical framework developed in [66] for 1D, 2D and RA systems has been applied to
analyze the performance and basic constraints of passive interferometric imaging for closerange applications. Close range system parameters have been set as a tradeoff between radiometric sensitivity, imaging rate and boresight spatial resolution, that has been presented as
the close-range uncertainty principle. It has been shown that, when compared with the same
front end parameters, spatial resolution and imaging rate, 2D-SA, 1D-SA and RA radiometric
sensitivity is equivalent and not a driver to select one of the options. However, off-boresight
radiometric resolution degrades as a function of ξ 2 + η 2 in the synthesized cases.
Close attention has been paid to analyze close-range radiometric sensitivity, which is critical to achieve both high imaging rates and good spatial resolution. The accurate radiometric
sensitivity expression recently validated within the Soil Moisture and Ocean Salinity (SMOS)
project [61] has been used , and its consistency to the approximate formula widely used in
passive interferometry [66] has been demonstrated. It has been shown that the optimum performance is achieved when imaging at a fixed range and the HPBW of each single antenna
in the array matches the scene FoV. Also, that this condition is always feasible, in a first
approach, independently of the imaging geometry and requirements.
Simulations and theoretical analysis have shown that close-range imaging with moderate
requirements is feasible with relatively simple front end configurations if some degree of offaxis performance degradation is allowed. Additionally, section 3.3 has discussed the path to
achieve more stringent specifications (e.g. ∆x ∼
= 1 K and ts 1 s) on the
= 1 cm, ∆TB ∼
penalty of higher cost and complexity. It is known that mmW screener applications benefits
from the penetrating capability of the electromagnetic fields. The simulations in this work
has been used to illustrate the main features and constraints of close-range synthetic aperture
imaging to show that, due to the small array size, mmW operation also allows for very large
predetection bandwidths and close-range configurations to improve radiometric sensitivity
while minimizing decorrelation effects and NF distortion.
It can be concluded that an sparse 1D-SA radiometer can be used with a moving walkway
to perform personnel screening avoiding mechanical movements with an optimum number of
mmW receivers. The performance of this screener in terms of ∆x, ∆T and ts is equivalent
to the performance of an screener based on a 2D-SA or a 1D-SA radiometer. However, using interferometric radiometers at mmW frequencies is still a challenge due to the required
Intermediate Frequency (IF) processing. This conclusion motivates the research presented
in chapter 4, where a technique to reduce the complexity of a mmW screener system is described.
56
Chapter 3
C HAPTER 4
One-dimensional Synthetic Aperture Radiometer
with Optical Signal Processing
C
HAPTER 3 concludes that the one-dimensional sparse interferometric radiometer achieves
a good tradeoff between radiometric performance and number of receivers for closerange screening purposes. However, still a major drawback resides on this type of radiometer: the acquisition of multiple correlations of large bandwith signals required to retrieve the
visibilities of the scene. This is a huge problem when the bandwith of the signals is on the order of several GHz if traditional techniques such as digital signal correlation or Intermediate
Frequency (IF) analog correlation are used [68] [69]. Specifically, if digital correlation technique is chosen, Analog-to-Digital Converters (ADCs) with a sampling frequency of fs = 2B
should be used in order to fulfill Nyquist criteria. Additionally, the correlations are performed
in Field Programmable Gate Arrays (FPGAs) that should process the large amount of data incoming from the ADCs. If the bandwidth of the signals are on the order of several GHz, the
hardware complexity required by the correlator system is unaffordable since neither FPGAs
nor ADCs supporting such large digital speed rate are commercially available.
This chapter describes a method to overcome the problem of routing and correlating all
the antenna signal pairs in an interferometric radiometer by upconverting the Radiofrequency
(RF) signal to the optical domain. Hence, the relative bandwidth of the modulated signal is
small (even with a RF bandwidth consisting of tens of GHz) allowing the use of commercially
available components for optical communications (e.g. Distributed Feedback (DFB) lasers,
photodiodes, couplers...). In addition, the distribution of the signal is simplified in the optical
domain with respect an RF distribution, since multiple optical signals can be guided either by
fiber optics or free-space avoiding coupling effects.
The first section of the chapter is devoted to describe the optical modulation and correlation process using LiNbO3 phase modulators. The working principle of the optical modulator is explained with the aim of understanding the characteristics of the modulated optical.
Moreover, the resulting expressions for an optical correlation of two radiometric receivers are
obtained for two different modulation schemes: 1) Double-Sideband (DSB) and 2) SingleSideband (SSB) modulations. In the second section of the chapter, the expressions governing
58
Chapter 4
Ele
od
ctr
es
ep
t
ara
ion
:d
Hot
e
lectr
ode
Grou
nd E
lectr
ode
LiNb
O3 c
ryst
Inte
al
d
uce
ract
io
n len
gth:
l
tica
Op
ave
lw
ide
gu
ield
E-F
Ind
Figure 4.1: Perspective schematic view of an x-cut optical phase modulator where the main parts (RF
electrodes, optical waveguide, LiNbO3 crystal...) are depicted.
the method are related with the classical interferometric theory. Both sections are complemented with measurements that confirm the validity of the expressions. Additionally, final
measurements consisting on one-dimentional images are acquired by moving two W-band
radiometric receivers along a line in order to synthesize the required baselines. The third
section is devoted to explain the optical distribution scheme that is able to obtain the signal
combinations between all receiver pairs. Finally, considerations regarding the performance
of the system are discussed at the end of the chapter for both types of optical modulations.1
4.1
Optical modulation
In order to up-convert the RF signal to the optical domain, a laser optical source is modulated
by the RF signal. There are mainly three types of commercially available optical modulator:
1) LiNbO3 modulators [70], 2) electro-absorption modulators [71] and 3) the direct modulation of a laser [72]. The study described in this chapter uses LiNbO3 modulators since they
achieve the maximum bandwidth among all the options [73].
4.1.1
LiNbO3 phase modulators
The LiNbO3 optical phase modulators are based in the electro-optical effect that occurs in
the LiNbO3 crystal. If the LiNbO3 crystal is placed between two electrodes, the phase of the
optical signal going through the crystal is modulated by the voltage V between the electrodes
1 The
following sections of this chapter may contain verbatim text and figures from [J1] [C3, C4].
4.1 Optical modulation
59
as
πn30 rV l
,
(4.1)
λ0 d
where d is the electrode separation, r is an electro-optic tensor that depends on the polarization of the optical beam, n0 is the LiNbO3 index of refraction, l is the length of the interaction
between the crystal and the optical signal and λ0 is the optical wavelength. Figure 4.1 shows
an schematic of a LiNbO3 phase modulator where the electrodes, the optical waveguide and
the direction of the electric field are depicted. The voltage required to produce a phase shift
of π is called half-wave voltage Vπ . The half-wave voltage is defined by the geometrical
characteristics of the modulator and is obtained directly from (4.1) as
∆Φ =
Vπ =
λ0 d
.
n30 r l
(4.2)
The orientation of the crystal axes with respect the optical waveguides and the electrodes
affects to the modulator efficiency and therefore to the half-wave voltage. The electric field
should be aligned with the z-axis of the crystal since it is the axis presenting the highest
electro-optic coefficient [70]. Figure 4.1 shows an schematic of an x-cut optical phase modulator where it is shown that the electric field created between the electrodes by the RF signal
generates an electric field parallel to the z-axis of the crystal. Additionally, LiNbO3 crystals
are birefringent and thus their refractive index depend on the polarization of the optical wave.
A consequence of the birefringence in the LiNbO3 crystal is that the modulation efficiency
of a LiNbO3 modulator also depends on the polarization of the incident optical wave. Hence,
an optical polarization control is required to maximize the modulation efficiency.
4.1.2
Optical phase modulation by a CW signal
If an RF Continuous Wave (CW) signal defined by x(t) = V0 sin(ωm t + ψ) is used to modulate a laser beam with and electric field E(t) = E0 ej(ω0 t+φ0 ) , the signal coming out of the
LiNbO3 modulator is
Em (t) = E0 ej(w0 t+φ0 +m sin(ωm t+ψ)) ,
(4.3)
where m =
πV0
Vπ
and φ0 =
2πn0 l
λ0 .
The term ejm sin(ωm t+ψ) can be decomposed as
ejm sin(ωm t+ψ) =
∞
X
Jk (m)ejk(ωm t+ψ) ,
(4.4)
k=−∞
where Jk is the Bessel function of the first kind and order k. Therefore the resulting modulated signal spectrum contains multiple sidebands separated ωm from the optical center frequency ω0 . If the RF signal amplitude fulfils the condition V0 Vπ , the following approximations can be performed: Jk (m) ≈ 0 ∀ |k| > 1, J±1 (m) ≈ ± m
2 and J0 (m) ≈ 1.
Therefore (4.4) can be expressed as
m
ejm sin(ωm t+ψ) ≈ 1 + (ej(ωm t+ψ) − e−j(ωm t+ψ) ),
(4.5)
2
where only the carrier and the first sidebands are considered. Introducing (4.5) in (4.3) the
optical signal is
Emod (t) ≈ E0 ej(ω0 t+φ0 ) [1 + jm sin(ωm t + ψ)] .
(4.6)
60
Chapter 4
Agere 2860 E
R=0.85
L m = 1.5 dB
Vπ =4.5 V
DSB
x1(t)
LiNbO3
Phase Modulator
b1(t)
Photodiode
E(t)=E 0·ej·w0·t
Laser
TIA
Polarizer
&
3 dB
Coupler
3 dB
Coupler
NEL NLK1556 STG
Optical power = 0 dBm
x2(t)
Transimpedance
Amplifier
Z=1200
Minicircuits
VLF -7200+
VHF-6010+
B = 2 GHz
fm = 7 GHz
LiNbO3
Phase Modulator
y (t)
DSB
DSB
b2(t)
L m = 1.5 dB
V π=4.5 V
Fujitsu FTM7921 ER
Power
Detector
p (t)
DSB
Rohde & Schwarz NRP-Z21
Figure 4.2: Optical modulation and detection schematic for two receivers. The optical signal provided
by a laser is modulated by the RF radiometric signals coming from the receivers. Two LiNbO3 modulators are used for this purpose. The DSB modulated signals are added and detected by a photodiode. The
resulting photocurrent contains the correlation between both receiver signals. The component model of
each part used in the measurement setup is specified.
Equation (4.6) approximates the result of the optical signal phase-modulated by a single RF
tone.
4.1.3
Cross-correlation of double-sideband optical modulated signals
Figure 4.2 shows a block diagram of the proposed optical conversion system. The RF signals
collected by the antennas in the millimeter-wave band are downconverted to provide x1,2 (t)
at an IF frequency compatible with the modulation bandwidth of the LiNbO3 phase modulator. The polarization of the optical signal produced by a DFB laser is adjusted by using
an optical polarizer to maximize the modulation efficiency of the LiNbO3 modulators as described in the previous section. The optical signals bDSB
1,2 (t) have been modulated respectively
by the IF radiometric signals x1,2 (t) and are combined and detected by a photodiode. The
photodetected current is amplified using a Transimpedance Amplifier (TIA) and the power of
the resulting signal is measured with a power detector.
Although (4.6) is derived for a single tone, the results are also valid when the modulating
signal is band-limited Gaussian noise with a small power [74] [75]. In this case, and going
4.1 Optical modulation
Sn1(f )
61
RF Domain
B
Sm2(l)
Sm1(l)
fm
So(l)
f
Optical Domain
Phase
Signal
Modulation
Optical Domain
Coupling
l0-lm
l0
l
Sidebands mixed with the carrier
in the photodiode
l
Sn1(f )+Sn2(f )
Sm1(l)+Sm2(l)
l0 l0+lm
Sm1(l)+Sm2(l)
Photodiode
RF Domain
B
Power
Detector
+
TIA
fm
DC Component with
the correlation value
f
Figure 4.3: Spectrum of the signal in each step of the modulation and detection process. The RF
spectrum of the signal coming from the receiver Sni (f ) modulates an ideal optical laser source So (λ).
The resulting modulated signal Smi is added to the modulated signal coming from other receiver Smj .
The result is mixed in a photodiode producing a signal with spectrum centered at fm and bandwidth B
proportional to Sni (f ) + Snj (f ). The final step is to measure the power of the signal with a power
detector. This process yields a DC component with the correlation between the RF signals coming from
both receivers.
back to the block diagram of Fig. 4.2, for an input signal of the modulator x1,2 (t) consisting
of a band limited Gaussian noise of bandwidth B, the modulated optical signal is given by
π
bDSB
(t)
≈
E
cos
(ω
t
+
φ
)
−
x
(t)
sin(ω
t
+
φ
)
,
(4.7)
0
0
i
i
0
i
i
Vπ Lm
where Lm corresponds to the optical losses in the modulator and xi (t) is defined as
xi (t) = nIi cos(ωm t) − nQi sin(ωm t),
(4.8)
being ni (t) = nIi (t) + jnQi (t) the equivalent baseband signal of the noise.
The following calculations are particularized for two front-ends and it is assumed that
n1,2 (t) are equal with a certain group delay difference n1 (t) = n2 (t − τ )e−jωm τ and with
equal power Pn1,n2 = Pn . Hence the correlation level of the RF signals modulating the
laser in each branch will depend on the delay difference τ . The effect of the receiver equivalent noise temperature and therefore the effect of additive uncorrelated noise in the result is
discussed in Section 4.1.5.
62
Chapter 4
In Fig. 4.2 the modulated optical signals bDSB
(t) and bDSB
(t) are combined using an
1
2
optical coupler and driven into a photodiode. The resulting photocurrent is amplified using
a TIA. The photo-conversion processing performs a non-linear operation that mixes the frequency of the sum bDSB
(t) + bDSB
(t) resulting in a DC component and multiple signal bands
1
2
of which only the ones falling inside the photodiode bandwidth ω = {ωm , 2ωm } are available. If a bandpass filter centered at ω = ωm is applied to the output of the TIA the resulting
signal is given by
√
C sin(∆φ)[x1 (t) − x2 (t)],
(4.9)
yDSB (t) =
2 2
πE RZ
where C = Vπ0Lm
being Z the transimpedance of the TIA, and R the responsivity of
the photodetector. Finally, the power of the filtered signal is described as

Z
Z
C
C
2
kyDSB (t)k dt =
sin2 (∆φ)  kn(t)k2 dt−
pDSB (τ, ∆φ) =
2T
2T
T
T


Z

−<
n(t)n∗(t − τ )e−jωm τ dt  ,
(4.10)


T
where n(t) = n2 (t), ∆φ = φ2 − φ1 is the phase difference between optical channels and
the symbol < denotes real part. Taking into account the properties of band limited noise the
power of the filtered signal becomes
pDSB (τ, ∆φ, ∆ψ) = C · Pn sin2 (∆φ)(1 − cos(∆ψ) · sinc(Bτ )),
(4.11)
where ∆ψ = ψ2 −ψ1 = ωm τ is the RF instantaneous phase difference. Note that (4.11) gives
the theoretical cross-correlation between x1 (t) and x2 (t) except for a phase shift of 180◦ and
a factor which depends on the optical phase difference ∆φ. By properly controlling ∆φ to
the fixed values ∆φ = π2 , 3π
2 , the measured power becomes
pDSB (τ, ∆ψ) = C · Pn (1 − cos (∆ψ) · sinc(Bτ )).
(4.12)
An schematic showing the spectrum of the signal in each of the intermediate steps of the
modulation and detection process is presented in Fig. 4.3.
4.1.4
Cross-correlation of single-sideband optical modulated signals
The main drawback of working with a DSB modulation resides in the necessity of maintaining the optical phase difference to ∆φ = π2 , 3π
2 . If only the correlation between two receivers
is needed, the phase control can be easily performed by applying a DC voltage to the phase
modulators. However, if the number of receivers is greater than 2, it is not possible to have
simultaneously all the optical channels with the required phase difference. Therefore the correlations of all receiver pairs cannot be computed at once. A possible solution is to use a SSB
modulation that, as will be shown in the following paragraphs, requires a phase difference
between optical channels of ∆φ = 0.
4.1 Optical modulation
63
FT{bi(t)}
Filtered
out
w0
w0-wm
w0+wm
w
E(t)
Optical signal
x i (t)
RF signal
LiNbO3
Phase Modulator
Optical Bandpass
Filter
b i (t)
SSB
b i (t)
Figure 4.4: Schematics of the filtering process required to obtain the SSB modulation. The top scheme
shows the frequency spectrum of the signal bi (t) with both sidebands. In this case, the lower sideband
is filtered out to obtain an upper-sideband modulation. The bottom scheme shows a block diagram with
the process required to obtain bSSB
(t).
i
In a SSB modulation, either the upper or the lower sideband created by the modulation
is suppressed. Figure 4.4 shows an schematics with the procedure required to obtain an SSB
modulation. In order to filter out one of the sidebands created by the phase modulation two
different techniques can be applied: the first consists on filtering out one of the sidebands
given by a phase modulator whereas the second consists on using an SSB modulator which
suppresses one of the sidebands in the modulation process [76]. In both cases, the complexity
of the system is increased: In the first case a an additional optical component consisting of an
optical filter should be added in each optical branch; and in the second case, the utilization of
an optical SSB modulator requires splitting the RF signal in two branches and switching the
phase 90◦ in one of the branches, thus requiring extra RF hardware.
In the case that the lower sideband is removed from the modulation the signal bi (t) at the
output of the modulator is expressed as:
bSSB
(t)
i
j(ω0 t+φi )
≈ E0 < e
1+
π
ni (t)ejωm t
2Vπ Lm
(4.13)
The signals coming from both modulators are combined, detected by a photodiode, amplified
by a TIA and filtered at ω = ωm . The resulting signal at the output of the filter is:
√
C
[(x1 (t) + x2 (t))(1 + cos(∆φ))+
2
+ sin(∆φ)(x01 (t) − x02 (t))]
y SSB (t) =
(4.14)
64
Chapter 4
−25
−30
dBm
−35
−40
−45
−50
Modulating signal
−55
Photodetected signal
−60
4
5
6
7
8
9
10
f [GHz]
(a)
(b)
Figure 4.5: (a) Photograph of the RF part of the setup used to prove experimentally eq. (4.11). The
noise signal generated by a noise source is amplified, filtered and split in two branches. One phase
shifter is used per branch in order to avoid signal decorrelation although only the phase of one branch
is swept. Two Bias-T are used to control the optical phase difference between paths by applying a DC
voltage to the modulators. (b) Spectrum of the RF noise signal used to modulate the optical laser (in
blue) and spectrum of the optical modulated signal mixed by the photodiode and amplified by the TIA
(in red). The resolution bandwidth of the measurement is 10 MHz.
where x0i (t) = < jni (t)ejωm t . If it is assumed that n1 (t) = n2 (t−τ )e−jωm τ and Pn1,n2 =
Pn , then the measured power is described by:
Z
SSB 2
1
SSB
y
p (τ, ∆φ, ∆ψ) =
(t) dt =
2T
T
= CPn (1 + cos(∆φ) [1 + sinc(Bτ ) cos(∆ψ − ∆φ)]
(4.15)
If the phase difference between optical channels is fixed to ∆φ = 0 the maximum output
power is achieved for a certain correlation level of the signals, yielding:
pSSB(τ, ∆ψ) = 2CPn [1 + sinc(Bτ ) cos(∆ψ)]
4.1.5
(4.16)
Optical correlation measurements of RF noise
This section presents a first experimental validation of the results obtained in Section 4.1.3.
The measurements presented in this chapter are performed using a DSB modulation since
the hardware requirements are lower. The results obtained with the DSB modulation are
used to validate the utilization of the optical technique with interferometric radiometers. The
conclusions obtained with those results can be directly extended to the method using a SSB
modulation since the principle of operation is the same. Figure 4.5(a) shows part of the
experimental setup used to perform the measurements, including the RF stage and the optical
modulators. The rest of the setup is included in the schematic of Fig. 4.2.
In order to test the optical correlator, the IF noise signals x1,2 (t) shown in Fig. 4.2
are synthesized by means of a broadband noise source with an equivalent noise temperature TN = 10000 K followed by 3 amplifiers of 24 dB. A bandpass filter centered at 7 GHz
4.2 Millimeter-wave interferometry measurements with optical signal processing
1
1
Theoretical
Normalized power
Normalized power
Measurement
0.8
0.6
0.4
0.2
0
0
50
100
150
200
∆φ [deg]
(a)
250
65
300
350
0.8
0.6
0.4
Measurement
Theoretical
0.2
0
0
50
100
150
200
250
300
350
∆ψ [deg]
(b)
Figure 4.6: (a) Measured signal amplitude (blue line) of the setup presented in Section 4.1.5 when
varying the IF phase ∆ψ with the phase shifter placed in the RF noise signal path while maintaining
∆φ = π2 . The theoretical curve (green dotted line) has been calculated using (4.12). (b) Measured
signal amplitude (blue line) of setup presented in Section 4.1.5 when varying the optical phase ∆φ by
applying a DC voltage to one modulator. The theoretical curve (green dotted line) has been calculated
using (4.11).
with approximately 2 GHz of bandwidth is placed just after the amplifiers. The signal is then
divided in two using an RF splitter, and phase shifters are introduced in each path to allow
changing their phase independently while preserving the symmetry between paths length,
thus preserving correlation. The signals coming out of the phase shifters are driven to the
optical modulators through a Bias-T to permit the use of a DC voltage to control the optical
phase difference ∆φ. Finally the signals from each modulator are combined using an optical
coupler and mixed in a photodiode. The detected photocurrent is then amplified using a TIA.
Figure 4.5(b) shows the spectrum of the RF modulating signal (blue line) and the detected
optical signal (red line) when both paths are combined. The measurement has been performed
just at the output of the optical receiver Agere 2860E shown in Fig. 4.2 using a Rohde &
Schwarz FSP40 spectrum analyzer. An equivalent noise bandwidth of 1.8 GHz centered at
7 GHz is achieved, and the whole optical stage attenuates the band of interest about 10 dB.
The experimental setup allows to modify the optical phase difference ∆φ and the RF
phase difference ∆ψ. Figures 4.6(a) and 4.6(b) show the relative variation of the detected
signal amplitude with ∆φ and ∆ψ respectively. The measured results are compared with the
expected behavior according to (4.11) and (4.12). A good agreement is obtained between
analytical results and measurements, which experimentally confirms the feasibility of correlating two RF signals in the optical domain. Furthermore, Fig. 4.6(a) shows the capability of
the system to keep the optical phase coherence.
4.2
Millimeter-wave interferometry measurements with optical signal processing
This section presents measurements performed using two independent radiometric front-ends
to synthesize the different baselines of a 1D interferometric radiometer array. Therefore in
this case, the signals n1 (t) = nc (t)+nu1 (t) and n2 (t) = nc (t−τ )+nu2 (t) are composed by
66
Chapter 4
a correlated nc (t) and an uncorrelated noise nui (t). The correlated part is the noise coming
from the scene that reaches both receivers and therefore is directly related with the antenna
temperature TA . The uncorrelated part is the noise generated by the receiver itself and is
related to the receiver noise temperature TR . If the noise power reaching each antenna is
considered equal, as well as the equivalent noise temperature of both receivers, the total
power at the output of the receivers are equal Pn1,n2 = Pn . If phasorial notation is used
for the noise, eq. (4.10) is transformed in the following expression for ∆φ = { π2 , 3π
2 } [54]


Z
1
p(τ ) =C< Pn −
nc (t)n∗c (t − τ )e−jωm τ dt
2T
T
ZZ
0
−j2πuξ
=C< Pn − S
TB (ξ, η)e
dξdη ,
(4.17)
where symbol < denotes real part and S = kB BG and
TB0 (ξ, η) =
TB (ξ, η)t(ξ, η)
p
.
Ωa 1 − ξ 2 − η 2
(4.18)
Decorrelation effects have been neglected (sinc(Bτ ) ≈ 1) for the sake of simplicity. By
including (2.26) in (4.17) the relation between the measured optical power and the scene
visibility becomes
p(u) = C (Pn − S<{V (u)}) .
(4.19)
Note that Pn can be several orders of magnitude higher than S<{V (u)} due to the equivalent
noise temperature of the receivers and therefore the dynamic range of the measurement is
strongly reduced. This issue cannot be calibrated since gain stability effects on Pn would
mask completely the calibration and the measurement of <{V (u)}. However this can be
solved by using the phase switching technique proposed in this section, which subtracts Pn
thus improving the quality and stability of the measurement.
4.2.1
Phase switching technique
The value of <{V (u)} can be directly obtained if a phase switching method is used [77].
If a phase shift of ψ0 = 180 ◦ is introduced to the output signal of one of the radiometric
receivers, the second term in equations (4.17) and (4.19) becomes positive. Hence, taking the
difference between two consecutive measurements with a phase shift ∆ψ0 = 180 ◦ between
them, the resulting value is given by
r(u) = 2CS<{V (u)}.
(4.20)
Hence, if the RF and optical parameters of the receiver are calibrated the value <{V (u)} can
be obtained. The phase switching technique can be implemented by either having a phase
shifter in each RF front-end and sequentially change between both phase states or by duplicating the optical channel with a difference of 180 ◦ . There is a tradeoff between complexity
and acquisition time, since duplicating the optical channel will reduce the acquisition time by
4.2 Millimeter-wave interferometry measurements with optical signal processing
67
a factor of 2. In the case of having a phase shifter, it can also be used to obtain the imaginary
part of the correlation by adding a phase shift of 90 ◦ between both receiver signals
r(u)|ψ0 =90◦ = 2CS={V (u)}.
(4.21)
An additional issue to consider in the phase switching technique is the effect of the gain
fluctuation of receiver amplifiers in the value of Pn . In order to subtract the value of Pn from
the measurement, the effect of gain variations must be canceled. This is achieved by setting
the phase switching rate faster than the gain variation. In our experiment, we have chosen
a switching rate of 50 Hz, above the gain fluctuation rate of our system. In order to have a
visibility integration time tv larger than the phase switching period, multiple measurements
are averaged.
4.2.2
Fringes created by a point source
An scene with a point source has been employed to validate the equations presented in the
previous section. The schematic of the scene setup is shown in Fig. 4.7(a). The fringe pattern
is measured by translating the point source along the x direction in the range of −2.5 cm <
xPS < 2.5 cm at a distance R = 25 cm from the antennas, for a fixed baseline u0 = 17.13.
η−ηi
i
In this case TB0 (ξi , ηi ) = TB0Ωt(ξa i ,0) Π( ξ−ξ
∆ξ )Π( ∆η ) where Π corresponds to a normalized
rectangular function. The antenna power pattern t(ξ, η) is considered to be constant along the
point source solid angle and the source is considered to be close to the boresight direction. In
this case (4.17) is expressed as:
STB0 t(ξi , 0)
p(ξi ) = C Pn −
∆ξ∆η cos(2πu0 ξi )sinc(u0 ∆ξ)
(4.22)
Ωa
and applying the phase switching technique, the correlation is:
r(ξi ) =
2CSTB0 t(ξi , 0)
∆ξ∆η cos(2πu0 ξi )sinc(u0 ∆ξ)
Ωa
(4.23)
An interferometric radiometer with two receivers has been built to test the capabilities
of the method with a wide bandwidth radiometric signal. The setup is shown in Fig. 4.7(b)
and Fig. 4.8, and it consists of two W-band front-ends to downconvert a 97 GHz signal to
a 7 GHz IF (the maximum operating frequency of the LiNbO3 modulator is 10 GHz). This
configuration can be simplified if a W-band LiNbO3 modulator is used [78]. The optical
scheme is the same one used in Section 4.1.5. The RF front-end consists of a W-band conical
horn antenna, with a beamwidth of 17.5 deg followed by a LNA; a double-balanced mixer
and a 2 GHz band-pass filter centered at 7 GHz; a chain of two amplifiers with a total gain
of 48 dB gain and a phase shifter to implement the phase switching technique between the
receivers. Finally the integration time for each fringe point has been established at 200 ms.
The point source consists of a ceramic resistor that has been warmed up to around 240 ◦ C.
Fig. 4.9 shows the resulting theoretical fringe pattern obtained with (4.23) plotted with the
measured response. It can be observed that the measurements matches with theoretical prediction, proving the suitability of the method with radiometric signals.
68
Chapter 4
er 1
eiv
c
e
R
D
t1
Point source
n
ten
An
er 2
eiv
c
e
R
a1
D
t2
n
ten
An
a2
u
R
xPS
x, x
(a)
(b)
Figure 4.7: (a) Schematic of the setup used in Sections 4.2.2 and 4.2.3. A point source based on a hot
resistor has been used as target to perform the measurements. (b) Photograph of the W-band and optical
setup built to perform the measurements described in Sections 4.2.2 and 4.2.3. The components of two
radiometric receivers are shown. The W-band components of each receiver are a conical horn antenna, a
LNA, a mixer and a x6 multiplier. The schematics of the receiver chain is described in Fig. 4.8 whereas
the optical part has been shown in Fig. 4.2.
4.2.3
One-dimensional image
A one-dimensional brightness temperature distribution has been imaged using the optical correlation method proposed in this paper with the same receiver architecture as in Section 4.2.2.
4.2 Millimeter-wave interferometry measurements with optical signal processing
69
IF Amp. Chain
2xMinicircuits ZX 60-183+
G: 48 dB
Mixer
Millitech MXP-10
CL: 12 dB
xi(t)
Conical Horn
BW: 17.5 deg
LNA
HXI HLNAW-241
G: 28 dB
NF: 6 dB
X6 Multiplier
Ducommun FMA-92
Output Power : 10 dBm @ 90 GHz
Rohde & Schwarz SMB 100A
x6
Phase shifter
Hittite HMC929
Bandpass Filter
Minicircuits
VLF-7200 +
VHF-6010+
Bandwidth = 2 GHz
Central frequency = 7 GHz
15 GHz
Figure 4.8: Schematic of the W-band receiver components. A conical horn with 17.5 deg of beamwidth
has been used as an antenna. A LNA with 28 dB gain and NF of 6 dB is placed before the mixer. The
7 GHz IF signal is filtered with 2 GHz of bandwidth and is amplified 48 dB. The last component before
the optical modulator is a phase shifter used to perform the phase switching described in Section 4.2.1.
40
r(ξ) [nW]
20
0
−20
Measurement
Theoretical
−40
−0.1
−0.05
0
0.05
0.1
ξ
Figure 4.9: Measured fringe pattern created by a point source at a distance of 25 cm with a fixed antenna
baseline of u = 17.13. The center frequency of the RF signal is 97 GHz as described in Fig. 4.8. The
measured values match with the analytical expression (4.23).
The radiometric front-ends have been mounted on linear stages to synthesize the baselines
corresponding to a linear array of antennas. The real part of the visibility samples have been
obtained from the correlation of the signals given by both receivers as described by (4.22)
integrating 200 ms for each visibility. In order to obtain the imaginary parts of the visibilities, a 90◦ phase shift has been added to one receiver signal. Moreover, before obtaining the
images a first calibration has been performed to retrieve the phase imbalance between both
receivers. In order to obtain the reconstruction of the scene the phase imbalance has been
70
Chapter 4
1
R(V) [K]
0.5
0
−0.5
−1
−17.3 −13.0 −9.4 −6.1 −3.0
0
5
10
15
u
20
Theoretical: x 25
=2.5 cm
src
T’ B [K]
I(V) [K]
src
=2.5cm
Measured: x src =3.4cm
src
0
9.4 13.0 17.3
Theoretical: x src =2.5cm
0.2
Theoretical: x =3.4 cm
0.5
6.1
Measured: x
Measured: x src=3.4 cm
1
Theoretical: x src =3.4cm
0.15
0.1
0.05
−0.5
−1
x[cm]
0 3.0
Measured: x src=2.5 cm
0
5
10
15
20
25
0
−0.5 −0.4 −0.3 −0.2 −0.1
(a)
0
0.1
0.2
0.3
0.4
0.5
ξ
u
(b)
Figure 4.10: (a) Measured real and imaginary parts of the scene visibilities for two different scenes
consisting on a point source placed at xPS = −2.5 cm and xPS = −3.4 cm from the origin. The
visibilities from u = 0 to u = 6 cannot be measured since the minimum antenna spacing is given by
the conical horn flange adapter of 22 mm. (b) The plot shows two reconstructed scenes obtained by
applying (4.24) to the measured visibilities shown in Fig. 4.10(a). The two different scenes consist of a
point source placed at xPS = −2.5 cm and xPS = −3.4 cm from the origin at a distance R = 30 cm
from the antennas.
corrected from the visibilities. An antenna separation of ∆u = λ/2 has been chosen in order
to avoid aliasing in the image as explained in Chapter 2.
The same ceramic resistor used in the previous section has been used as the point source
and it has been placed at a distance of R = 30 cm of the array. Two measurements have been
taken corresponding to two positions of the resistor, xPS = −2.5 cm (ξPS = −0.08) and
xPS − 3.4 cm (ξPS = −0.12) from the center of the array. A total of Nmu = 42 visibilities
have been measured corresponding to a synthetic array of 42 antennas. Figure 4.10(a) shows
the visibilities for u > 0 with an umax = 27. It must be noted that the visibilities in the
range 0 < u < 6 cannot be measured due to the flange of the conical horn antennas used in
the measurement, which forces a minimum baseline umin = 6. Nevertheless, the measured
visibility values agree with the simulated values. In order to retrieve the scene from the
measured visibilities the inverse Fast Fourier Transform (iFFT) is applied:
Z
0
TB (ξ) = V (u)ej2πuξ du
(4.24)
giving as a result the linear reconstruction shown in Fig. 4.10(b). The reconstructed image
matches with the position of the point source and roughly matches with the amplitude if
the system parameters described in Section 4.2.2 are used to calculate constants C and S of
(4.21).
A second scene has been measured with two resistors placed at xPS = −5.5 cm (ξPS =
−0.09) and xPS = 1.5 cm (ξPS = 0.02) from the center of the array at a distance R = 60 cm
from the antennas. Fig. 4.11(a) shows an infrared image of the scene revealing the physical
temperature of the resistors. After applying (4.24), the scene is reconstructed as shown in Fig.
4.11(b). A good agreement between the image and the scene is obtained.
4.3 Optical signal distribution for cross-correlation of multiple receivers
−34.6 −26.1 −18.8 −12.2 −6.0
71
x [cm]
0
6.0 12.2 18.8 26.1 34.6
1
T’ B [K]
0.8
0.6
0.4
0.2
0
−0.5 −0.4 −0.3 −0.2 −0.1
0
0.1
0.2
0.3
0.4
0.5
ξ
(a)
(b)
Figure 4.11: (a) Infrared image of a scene consisting on one resistor in vertical disposition placed
at xPS = −5.5 cm from the origin and one resistor placed horizontally at xPS = 1.5 cm. The
measured physical temperature of the resistors is around 200 ◦ C. The scene distance from the antennas
is R = 60 cm. (b) Reconstructed image from the scene shown in (a) obtained by applying (4.24) to the
measured visibilities. The response of both resistors, centered at xPS = −5.5 cm and xPS = 1.5 cm
from the center of the array respectively and at a distance R = 60 cm from the antennas.
4.3
Optical signal distribution for cross-correlation of multiple receivers
The measurements presented in Section 4.1.5 have been performed with two receivers. Nevertheless the optical modulation method presented in this paper allows the combination of
multiple receiver signals in the optical domain in order to perform the cross-correlation. The
combination can be performed in the free-space due to the possibility of guiding optical beams
with low divergence and with high spatial density. Moreover, the high level of integration of
optical components and waveguides make the optical signal routing affordable with no constraint on the RF signal bandwidth [79] [80]. The following section proposes a free-space
combination scheme for an arbitrary number of front-end receivers.
4.3.1
Distribution technique
Figure 4.12 show an schematics of the signal distribution system. The optical signals coming
from each modulator bi (t) are introduced to an optical splitter matrix having a number of
inputs equal to the number of receivers Nr and a number of outputs of 2Nr . This matrix is
equivalent to Nr sub-couplers, one for each optical channel, that is in charge of coupling the
input signal to 2 outputs with the same power level. The 2Nr output channels are distributed
using fiber optics towards collimating lenses that will emit the optical beam in a collimated
way. The Nr optical beams split by the optical splitter matrix, containing one of the two
beams split by each sub-coupler sbi2 (t), carried and grouped into collimating lenses that will
emit the beams with horizontal distribution. The Nr beams are introduced to a diffractive
beamsplitter that will divide each beam along the vertical axis in Nr sub-beams.
The beams produced by a diffractive beamsplitter are emitted with a certain angle, there-
72
Chapter 4
sb11(t)
sb Nr1(t)
Optical splitter matrix
hv1, hv2 ... hvNr
Cylindrical lenses
Diffractive beamsplitter
sb11(t)
sb12(t)
sb21(t)
sb22(t)
b2(t)
hh1, hh2 ... hhNr
sbNr1(t)
sbNr2(t)
s11, s12 ... s1Nr
s21, s22 ... s2Nr
View 2
sb Nr2(t)
Nr x 2Nr
bNr(t)
Ms
sb22(t) sb12(t)
b1(t)
sNr1, sNr2 ... sNrNr
Diffractive beamsplitter
Beamsplitter
View 1
Figure 4.12: Schematic of the distribution system. The optical signals bi (t) coming from the modulators enter to the optical splitter matrix placed at the left of the schematic. The output signal matrix
beams sij are driven to photodiode matrix shown in Fig. 4.14. The schematics of the points of view
“View 1” and “View 2” are shown in Fig. 4.13.
hv1, hv2 ... hvNr
Mv
s11, s21 ... sNr1
s12, s22 ... sNr2
sb22(t) sb12(t)
Mh
Beamsplitter
Beamsplitter
sb Nr2(t)
sb Nr2(t)
sb12(t)
hh1, hh2 ... hhNr
s1Nr, s2Nr ... sNrNr
View 2
View 1
Figure 4.13: Points of view “View 1” and “View 2” from the Fig. 4.12.
rs11, rs12 ... rs1Nr
s11, s12 ... s1Nr
Ms
fs11, fs12 ... fs1Nr
s21, s22 ... s2Nr
rs21, rs22 ... rs2Nr
fs21, fs22 ... fs2Nr
sNr1, sNr2 ... sNrNr
A/D
PC
Diode
Matrix
rsNr1, rsNr2 ... rsNrNr
fsNr1, fsNr2 ... fsNrNr
Figure 4.14: Schematics showing the opto-electronic conversion matrix, the filtering and amplifying
components and the power detector arrays.
fore in order to avoid the divergence of the beams a cylindrical lens is used to collimate the
beams along the vertical axis. This lens should be placed with the cylinder axis along the
horizontal plane and with a distance from the diffractive splitter equal to its focal distance. In
4.3 Optical signal distribution for cross-correlation of multiple receivers
73
Figure 4.15: Artist view of the multiplexing scheme. The red beam represents b1 (t) whereas the blue
beam represents b2 (t) . The purple beam is the result of adding b1 (t) + b2 (t). The artist view is
representative of the setup mounted in the laboratory to prove the suitability of the scheme.
such way the beams are collimated and the matrix M h is formed


b1 b2 · · · bNr
 b1 b2 · · · bNr 


Mh =  .
.. . .
..  .
 ..
.
.
. 
bNr b2 · · · bNr
(4.25)
The remaining N r channels sbi1 (t) split by the optical splitter matrix are transported,
grouped along the vertical axis, introduced in collimating lenses and emitted with vertical
disposition. Using a diffractive beamsplitter the beams are divided along the horizontal plane
creating Nr beams from each original beam an therefore creating a matrix of Nr xNr elements. Finally the beams are collimated using a cylindrical lens having the cylinder axis
along the vertical axis of the system. The process is equivalent to the one described in the
previous paragraph with the only difference that the resulting beam matrix Mv is rotated 90 ◦
with respect the matrix Mh


b1
b1 · · · b1
 b2
b2 · · · b2 


Mv =  .
(4.26)
..
..  .
..
 ..
.
.
. 
bNr bNr · · · bNr
Figure 4.13 clarifies the beam distribution in this part of the system. In a final step, the beam
matrices Mh and Mv are driven to a beamsplitter plate in order to combine the beams and
74
Chapter 4
obtain a sum matrix Ms

b1 + b1
b1 + b2
..
.


Ms = 

b1 + bNr
b2 + b1
b2 + b2
..
.
···
···
..
.
b2 + bNr
···

bNr + b1
bNr + b2 

.
..

.
bNr + bNr
(4.27)
The final step in the correlation process is based on the detection of the signal contained in
each optical beam. Figure 4.14 shows that a photodetector matrix is used to obtain the mixing
between the optical carrier and the optical sidebands for each element of Ms . Each photodetector is followed by a TIA in order to convert the current signal given by the photodetector
to a voltage signal with a certain transimpedance gain. Following the TIA a filter with the
same passband as the original RF signal is placed. The resulting signal at this point is given
by 4.9 or 4.14 if either DSB or SSB modulations are used respectively. The final step consists
of measuring the power by using an array of power detectors. The resulting matrix contains
the real part of the visibilities and is given by the following matrix for a DSB modulation


V11
V21 · · · VNr 1 






 V12
V22 · · · VNr 2 


).
(4.28)
Mv = C(Pn − S<  .

.
.
.
..
..
.. 

 ..






V1Nr V2Nr · · · VNr Nr
The following step is to perform the phase switching technique to remove Pn from the result.
It should be pointed out that the lower triangular matrix is redundant and it is not necessary
to be measured. The main drawback of this method is the strong alignment requirements of
the optical devices. Moreover, the phase variations in the fiber makes the proposed scheme
unfeasible without a phase control on each channel. Both issues can be solved if the scheme
is integrated and implemented with photonic waveguides. Figure 4.15 shows a 3D representation of the proposed optical signal distribution scheme.
4.4
System Performance Considerations
The performance of the system in terms of radiometric sensitivity is described in this section
taking into account the contribution of optical correlation process and the phase switching
technique. In addition, the image acquisition time is studied depending on the optical modulation scheme and system parameters to foresee the suitability of the method when real-time
imaging is required.
4.4.1
Radiometric sensitivity
The main noise sources in the system are the thermal noise generated in the receiver chain,
the shot noise generated in the photodetector and the receiver gain variations falling in a phase
switching period. The effect of the shot noise of the photodetector is neglected in front of the
thermal noise generated in the receiver front-ends since this is pre-amplified in the RF stage.
4.4 System Performance Considerations
75
1
1.1
Measured
Theoretical
Moving average
0.6
0.4
0.2
1
0.95
0.9
0
50
100
150
0.85
200
0
50
100
tv [ms]
(a)
200
250
(b)
0.7
1.4
Angular resolution
0.6
1.2
DSB
SSB
0.5
t s [s]
150
∆ψ [deg]
1
0.4
0.8
0.3
0.6
0.2
0.4
0.1
0.2
0
0
10
20
30
∆θ x [rad]
0
Theoretical
1.05
σv [K]
σv [K]
0.8
0
40
N mu
(c)
Figure 4.16: (a) Standard deviation of a visibility measurement σv depending on the integration time
tv . The noise received by the antennas is purely uncorrelated. The measurement is compared with the
theoretical values provided by (4.29). (b) Standard deviation of a visibility measurement σv depending
on the signal correlation level for an integration time tv = 2 ms. The phase of the IF signal is shifted
260 deg with steps of 3 deg to sweep the correlation level of the noise radiatied from a resistor point
source. A moving average of 20 samples is calculated from the measured points. The measurement is
compared with a theoretical curve calculated using (4.29). (c) Image acquisition time ts depending on
the number of antennas Nmu for a ∆T = 1 K. The system parameters are TA = 300 K, TR = 1000 K
and B = 1.8 GHz. The angular resolution ∆θx of the synthesized array is also depicted to show the
tradeoff between spatial resolution and radiometric sensitivity.
The phase switching rate is selected to avoid the gain fluctuations of the front-end receiver
components as well as to avoid variations in the laser amplitude. If a high gain LNA is placed
at the front of the chain as in our case, TR is mainly fixed by the noise figure of the LNA. The
resulting standard deviation for a single visibility measurement if DSB modulation is used is
given by
σv =
TAu + TR − TAc cos(∆ψ)
√
Btv
[K],
(4.29)
where TAu and TAc are respectively the equivalent temperature of the uncorrelated and correlated noise captured by the receiver antenna. The visibility integration time tv is the sum of
multiple phase switching periods. In the measurements performed in the previous sections,
the integration time is tv = 200 ms corresponding to 10 repetitions of a phase switching period of 20 ms. In order to validate (4.29), the visibility standard deviation has been calculated
from visibility samples measured with the system described in Section 4.1.5.
76
Chapter 4
Figure 4.16(a) shows the standard deviation of measured visibility samples for different
integration times tv . An absorber has been used to have a constant source of uncorrelated
noise in front of the antennas (TAc = 0 K). The values of S and C used to obtain the visibility value from the measured power (4.21) are those used in Section 4.1.5. The theoretical
curve has been calculated using (4.29) with TAu = 300 K, TAc = 0 K, TR = 1400 K (corresponding to a N F = 7.7 dB) and B = 1.8 GHz.
Additionally, the dependance of the visibility standard deviation with the correlation level
(TAc = 60 K) of the signals is shown in Fig. 4.16(b). A point source consisting of a resistor
has been used to radiate correlated noise. In order to modify the correlation level of the
processed noise signals, a phase sweep of 260 ◦ in steps of 3 ◦ has been performed using the
phase shifter placed in the receiver chain. A set of 1000 visibility samples has been measured
consisting of two phase switching periods of 1 ms yielding a total integration time of tv =
2 ms. These samples have been used to calculate the standard deviation of the visibility
for different values of phase shift. A moving average of 20 samples has been calculated to
clearly observe the sinusoidal behavior. The measurement is compared with a theoretical
curve calculated using (4.29) with TAc = 60 K, TAu = 400 K, TR = 1400 K and B =
1.8 GHz.
4.4.1.1
Image acquisition time
If a DSB modulation is used in the conversion process the phase shift between receiver channels ∆φ should be maintained to { π2 , 3π
2 } as stated in Section 4.1.3. Therefore, an imaging
system composed by Nmu > 2 receivers is not able to measure all the visibilities simultaneously since it is not possible to have the required phase shift between all the receiver pairs
at once. A solution is to repeat the measurements in order to cover the whole set of combinations. It can be shown that for Nmu receivers, it is required a minimum of dlog2 (Nmu )e
steps, where d·e denotes the ceiling value. Therefore the image acquisition time ts depends
on the number of receivers as ts = tv dlog2 (Nmu )e, leading to a radiometric sensitivity
TA + TR p
∆TDSB = 1.4 √
Nmu dlog2 (Nmu )e.
Bts
(4.30)
A different approach is either to use a SSB modulation or to filter one of the sidebands, thus
adding complexity to the system. In this case the optical phase shift required to perform the
correlation is ∆φ = 0, and the complete set of visibilities could be measured at once (ts = tv )
yielding
TA + TR p
∆TSSB = 1.4 √
Nmu .
(4.31)
Bts
Figure 4.16(c) shows the image acquisition time and angular resolution depending on the
number of receivers for a ∆T = 1 K. From the figure, it can be seen that for a particular case
with an spatial resolution of 3 cm at a distance of 1 m from the antennas, the required number
of antennas is Nmu = 36. For this system, a DSB modulation increases the acquisition time
by a factor of 6 compared with the SSB modulation.
4.5 Conclusions
4.4.1.2
77
Comparison with other available correlation techniques
The optical correlation technique described in this paper is similar to an RF analog correlation [58]. In both cases the correlation is performed by measuring the power of the combination of the received signals. The main difference resides in which domain the signal
is distributed in order to obtain the combination of all receiver pairs as required in aperture
synthesis interferometry.
There are several advantages of distributing the signals in the optical domain: 1) the signals can be distributed in the free space with collimated optical beams thus avoiding signal
couplings and uncontrolled radiation that could appear with RF signal distribution; 2) photonic integrated devices can be used to incorporate the whole distribution system in a compact
device; and 3) the bandwidth is limited by the optical modulator and can be of several tens of
gigahertz whereas in the RF distribution the bandwidth would be limited by the complexity
of the distribution components required to support large relative bandwidths. Nevertheless,
in practice the optical system requires a real-time phase control to maintain fixed ∆φ, representing a drawback in front of the RF correlator.
An additional technique commonly used in interferometric radiometry consists on sampling the RF signals with 1-bit precision and performing the correlation in a field programmable
gate array (FPGA) [81]. In this case the number of receivers Nr and the capacity of the FPGA
limits the bandwidth, and therefore limits the real-time imaging capabilities of the system.
Taking into account that the signal should be digitized with a sampling frequency of fs = 2B
to fulfill Nyquist criteria, the amount of internal data that the FPGA should manage is related
with fs Nr kbps. Hence, an interferometric system with a bandwidth of several GHz would
require a huge processing system [82] that are not affordable for screening systems.
4.5
Conclusions
This chapter presents a method to perform cross-correlation of RF radiometric signals in the
optical domain. The expressions governing the method are derived relating the results to the
classical interferometric imaging theory. In addition, the experimental validations prove the
suitability of the method to perform millimeter-wave passive interferometric imaging: 1) the
fringe pattern of a moving point source has been measured using a single baseline obtaining a
result that matches with the theoretical expressions; and 2) linear interferometric images have
been acquired by translating two receivers to sequentially synthesize the baselines of a filled
array of receivers, where the whole set of visibility samples have been obtained performing
the correlation in the optical domain.
With respect to the performance of the system, it has been shown that the receiver temperature TR of the system is not critically degraded by converting the signal to the optical
domain since the LNA placed at the front-end fixes the noise figure for the whole receiver
chain. This statement is supported in Section 4.4 with the calculation of the standard deviation of a visibility measurement σv , showing that the optical processing has no significant
influence on the radiometric performance of the system. In addition, the dependance of the
visibility standard deviation with the signal correlation level has been also supported with
measurements in Section 4.4.
78
Chapter 4
Additionally, Section 4.1.3 shows that if DSB modulation is used, the optical channels
should have an optical phase difference fixed to ∆φ = { π2 , 3π
2 }. This has a direct impact
on the image acquisition time since the visibilities cannot be acquired at once, representing
an increment of dlog2 (Nmu )e with respect to SSB modulation. Hence for systems with high
number of receivers an SSB modulation should be used (adding complexity in the optical
modulation hardware) in order to achieve real-time imaging with bandwidths in the order of
the GHz.
Terahertz Imaging and
Spectroscopy
C HAPTER 5
Terahertz Tomographic Imaging
combination of diffractive THz tomography of a sample with its spectroscopic information has been investigated and the results are presented in this chapter. An algorithm
based on the Born approximation has been used to retrieve 2-dimensional cuts of the sample.
This method is based on filling the image spectrum by performing electric field measurements
of the sample from different points of view. Once the image is reconstructed by applying an
inverse Fast Fourier Transform (iFFT), each pixel contains the absorption spectrum of the
material at that position. Section 5.1 shows the theoretical background of the diffractive tomography algorithm used to retrieve the images.
T
HE
In order to test the reconstruction algorithm and to foresee the results, an electromagnetic simulation of the imaging scenario has been performed using the commercial simulator
COMSOL Multiphysics. This simulator includes a 2-dimensional solver, thus allowing the
simulation of scenarios (constant in z axis) that would be unaffordable for a 3-dimensional
solver in terms of memory. The simulation setup and the results are presented in section 5.2
where the capabilities of the algorithm in terms of material detection are validated.
The third part of the chapter include THz measurements of different pharmaceutical compounds acquired with two different systems: 1) a time-domain spectroscopy system and 2)
a frequency domain THz system. The first system has been used to measure the absorption
spectrum of the compounds used as a sample in the imaging scenario whereas the frequency
domain system has been used to perform the tomographic measurements.
On the one hand, the full absorption spectrum has been measured by using the timedomain spectroscopy system due to several reasons: 1) the THz path is purged with nitrogen
thus avoiding the influence of the water vapor in the measured spectrum; 2) the dynamic
range in the higher frequency range of the THz band is higher, as well as the total frequency
range that extends up to 3 THz and 3) the frequency axis is precisely extracted due to the high
accuracy of the linear delay stage.
On the other hand, the tomographic measurements have been performed with the frequency domain system since the fiber coupling of the Photoconductive Switch (PCS) allows
the free movement of the antennas. Since the system consists on 1 transmitter antenna and
82
Chapter 5
1 receiver antenna, rotation movements should be performed to measure the required points
of view required to apply the reconstruction algorithm. Section 5.3 describes the measurement setup and presents the reconstructed tomographic images that show the detection and
identification capabilities of the reconstruction algorithm introduced in this chapter.
5.1
Terahertz diffraction tomography
The imaging algorithm used to reconstruct the tomographic images appearing in this chapter
is based on the Born approximation [83]. This approximation was first introduced in 1925 by
Max Born in order to solve problems related with the scattering of atomic particles. It consists
on a first-order approximation of a second-order differential equation (the inhomogeneous
wave equation) that governs the electromagnetic field distribution in the object to be imaged.
The method described in this section is based on illuminating the sample with a plane
wave and measure the field diffracted and scattered by the sample. The approximation is
valid if the condition d∆n < λ4 (where d is the sample diameter and ∆n is the permittivity
contrast between the sample material and the air) is fulfilled. Therefore, for a fixed sample
size, as the frequency increases the permittivity contrast should decrease in order to fulfill the
approximation.
Both the simulations and the measurements presented in this chapter do not fulfill the
approximation. In practice, this means that no absolute information can be obtained from
the images. Nevertheless, the relative information can be extracted to identify the sample
component without absolute quantification. A different technique is usually used if absolute
information is required: THz Computed Tomography (CT). CT uses a straight ray approach
for the image reconstruction, however this is an assumption that is not always correct at THz
frequencies.
The algorithm assumes that the sample properties does not vary in the z axis. The image
consists on a bidimensional reconstruction of a sample slice in the (x, y) plane. Moreover,
if the antennas are linearly polarized in the z axis direction, the electric field and the current
vectors are described by scalar field equations.
5.1.1
Reconstruction algorithm
The sample physical property that interacts with the electromagnetic waves is its complex permittivity, defined for a lossy material as (~r) = 0 + j ωσ , where σ is the material conductivity.
The field scattered by the sample Es (~r) is defined as
Es (~r) = E(~r) − Ei (~r),
(5.1)
where Ei (~r) is the electric field impinging to the object and E(~r) is the total field. The
scattered field can be expressed as the field generated by the equivalent currents on the sample
ZZ
Es (~r) =
−jωµ0 J(r~0 )G(~r − r~0 )dr0 ,
(5.2)
S
5.1 Terahertz diffraction tomography
Sample
Rotation
Q0
Transmitter PCS
83
Receiver
Rotation Path
Q
Rotation axis
z
Collimating Lens
Rotation Path
Q
Transmitter
Collimating Lens
Receiver
Collimating Lens
Scattered field
Fixed Position
Sample
Receiver PCS
y
x
Figure 5.1: 2D simulation geometry consisting on a Rohacell cylinder containing two cylinders filled
with two different compounds Ph1 and Ph2.
where G(~r − r~0 ) is the Green’s function and
J(r~0 ) = −jω((r~0 ) − 0 )E(r~0 )
(5.3)
is the induced current on the sample. By applying a bidimensional Fourier transform, the
angular spectrum of the currents is obtained
ZZ
~
˜ ~k) =
J(
J(~r)ej k~r d~r.
(5.4)
S
The following assumptions are taken from now on:
• The field scattered by the object is negligible in front of the incident field (Born approximation): (~r) ≈ 0 and therefore E(~r) ≈ Ei (~r)
~
• The object is illuminated by a plain wave with an incidence angle θ0 : Ei (~r) = e−j kθ̂0 ~r
where θ̂0 is the unit vector in the θ0 direction.
In addition C̃(~k − k0 θ̂0 ) is defined as the bidimensional Fourier transform of the contrast
r)
function C(~r) = 1 − (~
0 , Hence, the resulting expression after introducing (5.3) in (5.4)
evaluated at |k| = k0 is
˜ ~k) = −jω0 C̃(~k − k0 θ̂0 ).
J(
(5.5)
The reciprocity theorem states that the integral of the currents radiating on a volume va multiplied by the electric field generated by currents on a volume vb , is equal to the integral of
84
Chapter 5
the currents radiating on a volume vb multiplied by the electric field radiating from currents
on the volume va [84]
ZZ
ZZ
~
~
~ a dvb .
Ja · Eb dva =
J~b · E
(5.6)
va
vb
In the scenario shown in Fig. 5.1, it is assumed that Jb corresponds to the currents induced on
the sample by the electric field Ei (~r; θ̂0 ) and Ja are the currents on the transmitter antenna.
In addition, Jb radiates the scattering field Es (~r) whereas Ja radiates a plane wave e−jk0 θ̂·~r .
Therefore, from (5.3) the currents induced in the sample from the incoming field E(~r; θ̂0 ) is
described by
Jb (~r) = −jω0 C(~r)E(~r; θ̂0 ).
(5.7)
From (5.5) and using (5.6) the following expression is obtained
Z
C̃(k0 (θ̂ − θ̂0 )) = jωµ0
Ja (~r, θ)Es (~r; θ̂0 )dva .
(5.8)
va
If a cylindrical measurement geometry as presented in Fig. 5.1 is considered, (5.7) is expressed as
Z 2π
C̃(k0 (θ̂ − θ̂0 )) = jωµ0
I(θ − σ)Es (σ; θ̂0 )Rdσ,
(5.9)
0
where I(θ − σ) is the current distribution along an angular position σ of the antenna that
radiates a plane wave with θ direction. This current distribution can be expressed, for an
arbitrary radius of the cylinder geometry as
I(θ − σ) = −
∞
X
j −n
2
ejn(θ−σ) ,
ωµ0 Rπ n=−∞ Hn(2) (k0 R)
(5.10)
(2)
where Hn is the Hankel function of the second kind and R is the radius of the cylindrical
geometry. In addition, the scattered field considering a plane wave impinging to the object
can be expressed as
Z 2π
Es (σ; θ̂0 ) =
I(θ0 − σ0 )Es (σ; σ0 )Rdσ0 ,
(5.11)
0
where Es (σ; σ0 ) is the scattered field measured at an angle σ and produced by a incident
wave coming from the direction σ0 .
Considering that both receiver and transmitter antennas are placed further than the farfield
2
distance from the sample (R >> 2D
λ ), (5.10) can be approximated asymptotically by
s
π
2k0
I(θ − σ) = −
δ(θ − σ)e−j(k0 R− 4 ) ,
(5.12)
2
2
πRω µ0
where δ() is the Dirac delta function. Finally, by applying (5.12) and (5.11) to (5.9), the
resulting expression is
Z
Z
2Re−jk0 R 2π 2π
C̃(k0 (θ̂ − θ̂0 )) =
δ(θ − σ)δ(θ0 − σ0 )Es (σ; σ0 )dσdσ0 ,
(5.13)
Z0 π
0
0
5.2 Imaging scenario simulations
85
kcy
−20
-k0
kx< 0
kx> 0
2k0
kcx
kcy [rad/cm]
−10
0
10
20
−20
-k0
−10
0
10
20
kcx [rad/cm]
(a)
(b)
Figure 5.2: (a) Angular spectrum of the contrast function C(~
r) for a fixed incidence angle θ0 . The black
curve corresponds to the contrast profile given by the forward scattered field (−90 < θ < 90) deg.
(b) Angular spectrum of a reconstructed image for θ0 = 45n deg where 1 ≤ n ≤ 8 and -30 ≤ θ ≤
30 deg.
where the final result after the integration is
C̃(k0 (θ̂ − θ̂0 )) =
2Re−jk0 R
Es (θ; θ0 ).
Z0 π
(5.14)
Figure 5.2(a) shows an schematic that illustrates how the measured field is translated
to the angular spectrum of the sample image contrast. The electric field value Es (θ; θ0 ),
scattered by the sample in the direction θ0 when an incident plane wave impinges from the
direction θ, corresponds to the contrast spectrum value with angular coordinates ~kc = k0 (θ̂ −
θ̂0 ). It should be pointed out that the high frequency part of the spectrum is filled with the
electric field values backscattered by the sample given by receiver antennas placed at θ ≈ −θ0
(reflection geometry), yielding a maximum frequency of 2k0 . The low frequency part of the
spectrum corresponds to forward scattered electric field and is measured when the receiver
antennas are placed at θ ≈ θ0 (transmission geometry).
Figure 5.2(b) shows the spectrum of a retrieved image. It corresponds to a reconstruction
of a measurement with θ0 = 45n with n = 1...8 and −30 < θ < 30 in steps of 1 deg.
Note that the semi-circles are not well defined since the spectrum is convolved by the spectral
response of the rectangular window applied due to the truncation of the reconstructed image.
5.2
Imaging scenario simulations
This section includes electromagnetic simulations that are used to foresee the behavior of
the algorithm in the THz range for a certain scenario. The Finite Element Method (FEM)
86
Chapter 5
simulator COMSOL Multiphysics [85] has been used to obtain the scattered fields for several incident and reception angles. In order to simplify the simulation and due to the high
simulation frequency a two-dimensional geometry has been used. This geometry assumes
uniformity in the z-axis, reducing the physical space where the electric field should be calculated. This simplification of the problem is crucial to enhance the acquisition speed in
scenarios of several tens of wavelengths.
5.2.1
Simulation scenario
Figure 5.3 shows the geometry introduced into the simulator to retrieve the scattered fields. It
consists on several cylindrical sections that represents different materials in a two-dimensional
geometry. The main sample consists on a 12 mm diameter cylinder of Rohacell material (r ≈
1.05) where two inner-cylinders have been filled with two different materials Ph1 and Ph2.
Both materials have the same real permittivity but different loss tangent r = 1.7(1−j tan(δ)
given by Fig. 5.4. The loss tangent is zero for all the simulated frequency range except at
500 GHz and 600 GHz for the material Ph1 and Ph2 respectively. The objective of introducing this dependance of the loss tangent with the frequency is to model absorption resonances in the materials. The scenario includes an air section that ends in a Perfect Matched
Layer (PML). The PML absorbs the scattered radiation avoiding undesired back-reflections,
thus emulating a free-space environment.
As an excitation, a plane wave depending on the incidence angle θ0 as
Eiz (θ0 ) = e−jk0 (x cos(θ0 )+y sin(θ0 ))
(5.15)
is included in the model. The currents induced by the plane wave in the outer part of the
main cylinder are calculated by the solver. As a post-processing stage, the far-field radiated
by the induced currents are evaluated and are given as a main output of the simulator. The
algorithm presented in Section 5.1.1 is applied to the fields scattered by the object to reconstruct the image. The complete set of measurements are acquired in a three-dimensional
matrix with indexes (f, θ0 , θ), where f = 100, 200...800 GHz; θ0 = 0, 45, 90...315 deg and
θ = 0, 0.5, 1, ...359.5 deg with a total number of 46080 electric field points.
5.2.2
Spectroscopic imaging
In order to test the algorithm with a canonical shape, a first set of images that not include the
materials Ph1 and Ph2 have been reconstructed. In this case, the inner-cylinders have been
filled with air instead. Figure 5.5 shows the retrieved images frequency by frequency from
100 GHz to 800 GHz. The outer shape of the main cylinder is retrieved in all the images.
However, the shape of the inner-cylinders change drastically with the frequency. As the
frequency increases, the shape of the inner-cylinders is not well retrieved and for frequencies
greater than 500 GHz there is no clear difference in the image that leads to the identification
of the inner-cylinders. The image quality is reduced as the simulation frequency is increased
since the Born approximation loses validity. As the frequency is increased, the scattered
field is concentrated in values of θ close to the forward-scattering point (or pure transmission
point). This causes that the high spatial frequencies of the image are not properly retrieved,
translated into a poor reconstruction of the abrupt changes in the image.
5.2 Imaging scenario simulations
87
10
y [mm]
5
Ph2
0
Ph1
Rohacell
−5
Air
−10
PML
−10
−5
0
5
10
x [mm]
Figure 5.3: 2D simulation geometry consisting on a Rohacell cylinder containing two cylinders filled
with two different compounds Ph1 and Ph2.
Loss tangent (tand)
0.08
Ph 1
Ph 2
0.06
0.04
0.02
0
100
200
300
400
500
f [GHz]
600
700
800
Figure 5.4: Loss tangent against the frequency of the compounds Ph1 and Ph2.
In a second simulation trial, the materials Ph1 and Ph2 have been introduced in the scenario in order to study the impact of the frequency-variable loss-tangent in the reconstruction.
Figure 5.6 shows the retrieved images for each frequency. It should be pointed out a main
difference with respect the reconstruction of the images appearing in Figure 5.5: the reception
angle spans from −30 to 30 deg instead of covering the whole circumference. This restriction
in the reception angle has been introduced to simulate the measurements capabilities of our
system as will be described in Section 5.3.2. At first sight, it can be noted that the spatial
resolution of the images strongly depends on the frequency. As the frequency increases the
spatial resolution increases as well. This effect in the images is more noticeable in the images of Fig. 5.6 than in the ones appearing in Fig. 5.5 due to the restriction in the reception
angle. Regarding the appearance of the materials Ph1 and Ph2 in the image, no change is
observed depending on the frequency except at 500 GHz and 600 GHz where the absorption
peaks of the materials are placed. The image retrieved at 500 GHz shows a clear attenuation
88
Chapter 5
10
10
10
10
5
5
5
5
1
−5
−10
−10
0
0
x [mm]
5
−10
−10
10
(a) 100 GHz
0
−5
−5
−5
y [mm]
0
y [mm]
y [mm]
y [mm]
0.9
−5
0
x [mm]
5
−10
−10
10
(b) 200 GHz
0.8
0.7
0
0.6
0.5
−5
−5
0
x [mm]
5
−10
−10
10
(c) 300 GHz
0.4
0.3
−5
0
x [mm]
5
10
(d) 400 GHz
10
10
10
10
5
5
5
5
1
−5
−10
−10
0
−5
−5
0
x [mm]
5
−10
−10
10
(f) 500 GHz
y [mm]
0
y [mm]
y [mm]
y [mm]
0.9
0
−5
−5
0
x [mm]
5
−10
−10
10
(g) 600 GHz
0.8
0.7
0
0.6
0.5
−5
−5
0
x [mm]
5
−10
−10
10
(h) 700 GHz
0.4
0.3
−5
0
x [mm]
5
10
(i) 800 GHz
Figure 5.5: Reconstructed images from the tomographic simulation of the scene shown in Fig. 5.3,
however in this simulation the pharmaceutical compounds have not been considered and the innercylinders are filled with a air. Each image corresponds to a reconstruction of the contrast at a single
frequency: (a) 100 GHz, (b) 200 GHz, (c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz, (h)
700 GHz, (i) 800 GHz.
10
10
10
10
5
5
5
5
1
0
y [mm]
0
y [mm]
y [mm]
y [mm]
0.9
0
0.7
0
−5
−5
−5
−5
−10
−10
−10
−10
−10
−10
−10
−10
−5
0
x [mm]
5
10
(a) 100 GHz
−5
0
x [mm]
5
10
(b) 200 GHz
−5
0
x [mm]
5
10
0.8
(c) 300 GHz
0.6
0.5
0.4
0.3
−5
0
x [mm]
5
10
(d) 400 GHz
10
10
10
10
5
5
5
5
1
−5
−10
−10
0
−5
−5
0
x [mm]
(f) 500 GHz
5
10
−10
−10
y [mm]
0
y [mm]
y [mm]
y [mm]
0.9
0
−5
−5
0
x [mm]
(g) 600 GHz
5
10
−10
−10
0.8
0.7
0
0.6
0.5
−5
−5
0
x [mm]
(h) 700 GHz
5
10
−10
−10
0.4
0.3
−5
0
x [mm]
5
10
(i) 800 GHz
Figure 5.6: Reconstructed images from the tomographic simulation of the scene shown in Fig. 5.3.
In this case both compounds Ph1 and Ph2 have been considered in the reconstruction. Each image
corresponds to a normalized contrast reconstruction at a single frequency: (a) 100 GHz,(b) 200 GHz,
(c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz.
in the zone where the material Ph1 is placed whereas at 600 GHz the attenuation is shown in
the place where the material Ph2 is located. Hence, the variation in loss tangent has a clear
effect on the images and can be foreseen that a material with a certain absorption peak can be
5.2 Imaging scenario simulations
89
1
Normalized Contrast
0.9
0.8
0.7
0.6
Pharma 1
Pharma 2
0.5
0.4
100
200
300
400
500
f [GHz]
600
700
800
Figure 5.7: Reconstructed contrast depending on the frequency for both materials. The contrast has been
integrated along the area defined in Fig. 5.3 by the material Ph1 and Ph2 for the blue (continuous) and
green (dotted) lines respectively.
Dynamic range [dB]
60
50
40
30
20
100
200
300
400
500
f [GHz]
600
700
800
Figure 5.8: Dynamic range of the imaging setup based on the THz-CW system depending on the frequency.
identified in the image by using the proposed tomographic algorithm.
Additionally, the frequency response of the materials can be obtained by integrating the
zone where it is located against the frequency. Figure 5.7 shows the dependence with the
frequency of integrating the contrast zone where the materials Ph1 and Ph2 are located. The
attenuation points agree with the loss tangent peaks in each material. Thus, the spectroscopic
response of the materials can be extracted from the images. However, since the Born approximation is not fulfilled due to the high contrast of the materials Ph1 and Ph2 with the
Rohacell, the images do not provide quantitative information. Therefore parameters such material concentration cannot be provided by the images and only qualitative information can be
obtained.
An additional simulation has been performed introducing additive Gaussian noise to the
simulated results in order to achieve the same dynamic range as the one provided by the
measurement setup. Figure 5.8 shows the measured dynamic range of the imaging setup that
90
Chapter 5
10
10
10
10
5
5
5
5
1
−5
−10
−10
0
−5
−5
0
x [mm]
5
−10
−10
10
(a) 100 GHz
0
0
−5
−5
0
x [mm]
5
−10
−10
10
(b) 200 GHz
0.8
0.7
y [mm]
0
y [mm]
y [mm]
y [mm]
0.9
0.6
0.5
−5
−5
0
x [mm]
5
−10
−10
10
(c) 300 GHz
0.4
0.3
−5
0
x [mm]
5
10
(d) 400 GHz
10
10
10
10
5
5
5
5
1
−5
−10
−10
0
−5
−5
0
x [mm]
5
−10
−10
10
(f) 500 GHz
0
0
−5
−5
0
x [mm]
5
(g) 600 GHz
10
−10
−10
0.8
0.7
y [mm]
0
y [mm]
y [mm]
y [mm]
0.9
0.6
0.5
−5
−5
0
x [mm]
5
10
−10
−10
(h) 700 GHz
0.4
0.3
−5
0
x [mm]
5
10
(i) 800 GHz
Figure 5.9: Reconstructed images from the tomographic simulation of the scene shown in Fig. 5.3
adding complex Gaussian noise to the simulation to achieve the dynamic range shown in Fig. 5.8. Both
compounds Ph1 and Ph2 have been considered in the reconstruction. Each image corresponds to a
normalized contrast reconstruction at a single frequency: (a) 100 GHz,(b) 200 GHz, (c) 300 GHz, (d)
400 GHz, (f) 500 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz.
1
Normalized Contrast
0.9
0.8
0.7
0.6
Pharma 1
Pharma 2
0.5
0.4
100
200
300
400
500
f [GHz]
600
700
800
Figure 5.10: Reconstructed contrast depending on the frequency for both materials introducing additive
Gaussian noise. The contrast has been integrated along the area defined in Fig. 5.3 by the material Ph1
and Ph2 for the blue (continuous) and green (dotted) lines respectively.
is described in Section 5.3.1. It can be shown that as the frequency increases the dynamic
range decreases, starting from 50 dB at 100 GHz to 25 dB at 800 GHz.
If an additive Gaussian noise is added to the simulated electric field used to obtain the
images shown in Fig. 5.6, the resulting reconstructed images are presented in Fig. 5.9. It can
be noted that the reconstruction of the high frequency simulations yield noisy images since
the dynamic range is reduced to about 25 dB. Nevertheless, the spectroscopic behavior of the
samples is still perceived. This confirms the suitability of the measurement system, in terms
5.3 Measurements
91
of dynamic range, to measure the samples equivalent to the simulated ones.
The result of integrating the zones where both materials are located is shown in Fig. 5.10.
Despite the perception of the absorption characteristic of both materials is reduced, the peaks
at 500 GHz and 600 GHz for Ph1 and Ph2 respectively can be noted. From these simulations
can be concluded that, despite the reduction of dynamic range hinders the reconstruction of
the spectral behavior of the sample by the algorithm, still the detection and identification of
the materials can be performed.
5.3
Measurements
In order to validate the simulations and to study the performance of the algorithm with real
data, a set of measurements of different samples has been performed. The data required to
reconstruct the image has been measured using a THz-CW spectroscopy system whereas the
spectroscopic characterization of the sample has been performed using a Terahertz TimeDomain Spectroscopy (THz-TDS). Since both equipments are available in our laboratory, the
most suitable one has been chosen for each operation.
On the one hand the THz-TDS setup provides a better frequency accuracy than the THz-CW
due to the high precision of the delay stage incorporated in the system [27]. In addition, the
complete spectral response in amplitude and phase can be obtained from a sample using two
measurements: a reference and sample measurements. As a result, a complete spectral information of the sample can be obtained in 15 minutes approximately and with high accuracy.
On the other hand the THz-CW system used in this thesis relies on thermal tuning of
the optical frequency to shift the photomixed THz frequency [86]. The system software
incorporates a calibration file that associates a certain laser temperature to an output optical
frequency. The resulting THz radiation is given as a result of the photomixing of two laser
frequencies with a separation equal to the THz frequency: fTHz = fl2 − fl1 where f THz
is the THz frequency whereas fl2 and fl1 are the frequency of each laser source. Hence, by
using thermal tuning fl2 can be increased and fl1 can be decreased yielding a increment of
f THz or viceversa. Hence, the frequency accuracy relies on calibration quality of the system
and on its repeatability throughout time. In addition, due to the inherent inertia of the thermal
tuning, once a certain objective temperature is set in the laser controllers, around 15 minutes
should be waited until the frequency is properly set. Therefore, it makes extremely slow the
acquisition of multiple frequency point with complex data information.
Nevertheless, two main advantages makes this system a good choice for tomography:
1) the system is fiber-coupled, allowing a complete free movement of the photomixers as
required by the tomographic algorithm; and 2) once a certain frequency is set, a complex data
measurement lasts 1 second whereas in the THz-TDS the whole frequency spectrum should
be retrieved, even when only one frequency is required.
The following sections describe the measurement methodology required to obtain the field
scattered by the sample intended to be imaged. Additionally, several image reconstructions
that validate the algorithm are shown.
92
Chapter 5
Distributed-feedback
laser heads
Figure 5.11: Photograph of the THz-CW system laser heads.
Horizontal
stage
Sample rotation
servo
Horizontal linear stage
Servo sample
rotor
Sample
Rx photoconductive
switch
Sample
RF absorber
Rx lens
Receiver
rotor
Tx photoconductive
switch
z
y
x
(a)
(b)
Figure 5.12: Photographs of the tomographic measurement setup . The main components of the system
are presented in the photographs.
5.3 Measurements
5.3.1
93
Setup and sample preparation
The setup shown schematically in Fig. 5.1 has been implemented in the laboratory. As
mentioned in the last section, a THz-CW system has been used to acquire the multiple field
points required to reconstruct the image. The Distributed Feedback (DFB) lasers used to
produce the two optical tones with frequency fl1 and fl2 are shown in Fig. 5.11. Both
optical signals are coupled using a 2x2 optical coupling matrix, whose two outputs are the
combination of the two inputs signals, and driven to the receiver and transmitter PCS using
fiber optics. Figure 5.12 shows photographs of the measurement setup describing the main
components.
In Fig. 5.12(a), the transmitter photoconductive switch antenna. Note the fiber optics with
blue protective cover that couples the laser power into the antenna. Also the coaxial cable in
charge of biasing the antenna with a 13V, 7 kHz square signal is shown. The photoconductive
switch is mounted on two micrometer stages that allow vertical (z-axis) and horizontal (xaxis) displacement of the antenna. Furthermore, the whole antenna mount is held on a rail
that allows a continuous displacement in y-axis.
The sample is held by an optical post that is rotated by a winch servo. This servo, after a
proper calibration, can be rotated 360 ◦ with an accuracy around 1 ◦ . The control of the servo
is made by using a commercial control board Pololu Maestro 6-channel than can be connected
to a computed by a Universal Serial Bus (USB) port. A Polyvinyl Chloride (PVC) structure
holds the servo to a two-dimensional 300x300 mm2 horizontal linear stage used to translate
the sample. During the measurement, the sample is translated to two different positions: 1)
the measurement position, where the servo rotation axis and the receiver rotation axis match;
and 2) the empty chamber position, where the sample is translated to a maximum x-axis and
z-axis value to avoid any intrusion of the sample in the measurement. Note in the Fig. 5.12(a)
that an absorber has been placed covering the two-dimensional stage, trying to avoid undesired reflection from the metal parts that compose and hold the stages. A special care with
undesired reflections has been taken at low frequencies where the transmitted beam covers a
wide area. As the frequency is increased, the divergence angle of the beam is decreased and
the amount of undesired reflections decrease.
Figure 5.12(b) shows the receiver components of the setup placed on a rail. A Teflon
plano-convex lens has been used to capture the plane wave scattered by the sample. The scattered radiation is then concentrated on the receiver photoconductive switch aperture. A fiberoptics is used, as in the transmitter PCS, to couple the laser in the receiver PCS. However,
in the receiver antenna, the coaxial cable does not bias the antenna but collects the photoinduced current. The received current is amplified by a Transimpedance Amplifier (TIA) and
driven to the input of the lock-in amplifier. Since the receiver components should be rotated
around the sample, the rail is held on a rotation stage with the same rotation axis as the sample
rotation servo. This rotation stage is controlled via a USB port with the computer.
In the electronics reception stage, a lock-in amplifier is in charge of demodulate the received voltage given by the TIA. The THz electric field has been previously modulated at
7 kHz by the bias of the transmitter PCS, therefore the photo-induced current is as well modulated at the same frequency. The lock-in amplifier gets locked to the modulation frequency
and retrieves the amplitude value of the signal. This technique is commonly used to improve
the Signal to Noise Ratio (SNR) of the retrieved signal, that otherwise would be masked by
94
Chapter 5
Ø25mm
Rohacell Samples
Ø12mm
Rohacell
Ø12mm
Polaramine & Rohacell
Figure 5.13: Photograph of the different Rohacell blocks used as a sample for image reconstruction.
Flicker or 1/f noise. This method displaces the spectrum of the received signal out of the
influence of the Flicker noise achieving a better SNR in the reception.
In a final reception step, the signal at the output of the lock-in is introduced in a Analogto-Digital Converter (ADC) that is connected via a USB port to the computer. Note that the
whole measurement setup can be controlled with one computer allowing a fully automatic
acquisition of the several samples needed for the image reconstruction.
Regarding the samples preparation, the material chosen to build the samples is Rohacell
(r = 1.05). Figure 5.13 shows the different sample structures built to serve as a holder
for the pharmaceutical compound in the spectroscopic imaging process. In the image three
different structures are presented: 1) a 12 mm diameter solid Rohacell cylinder; 2) a 12 mm
diameter Rohacell cylinder filled with Polaramine in a inner-cylinder of 6 mm diameter; and
3) a 25 mm diameter Rohacell cylinder with two empty inner-cylinders of 6 mm diameter.
Several images have been taken from the described samples, varying the position and the
content in order to validate the reconstruction algorithm.
5.3.2
Complex data acquisition
The algorithm described in Section 5.1.1 requires complex information of each measured
electric field point in order to reconstruct the image from the scene. However, the THz-CW
system used to measure the field data does not provide direct information of amplitude and
phase of the THz. The resulting parameter given by the system is a Direct-Current (DC)
voltage signal Vm related with
Vm (A, φ) = A cos (kFO ∆lFO + kTHz rTHz + φ),
(5.16)
where A is the THz signal amplitude, kFO is the wavenumber in the fiber optics, ∆lFO is the
length difference of the section of fiber optics going from the 2x2 optical coupler to the PCS,
95
Modulation current
[ µA]
5.3 Measurements
300
0
0.16
t [s]
0.32
0.5
200
100
0
6
Measured voltage [V]
4
2
0
−2
−4
−6
200
200.05
200.1
200.15
f [GHz]
200.2
200.25
200.3
Figure 5.14: Acquisition trace from one trigger signal. The top Figure shows the laser modulating
current ramp whereas the bottom Figure shows the variation on the THz frequency produced by the
modulation.
kTHz is the wavenumber in the THz path (free-space), rTHz is the length of the THz path
and φ is the phase of the THz electric field. Note that the spectral response of the system is
no considered in (5.16).
With a single measurement, the value of A and φ cannot be retrieved. In practice three
different techniques can be used to retrieve the amplitude and phase of the complex THz
signal:
1. Either the receiver or transmitter PCS can be mounted on a mechanical delay stage
that translates the antenna 90 ◦ at the working frequency. Hence, two measurements
are done: 1) Vm0 without delay; and 2) Vm90 with 90 ◦ of delay.
p Using both measurements, the complex information can be obtained as A =
(Vm0 )2 + ((Vm90 )2 , and
V 90
φ = arctan( Vm0 ). The main drawback of this method is the necessity of an extra
m
linear stage to perform the delay, adding extra mechanical movements that may slow
down the acquisition speed.
2. The frequency of the THz radiation is swept few megahertz by thermal tuning of the
0
0
laser frequency. In this case a set of points of Vm (kTHz ) for kTHz = {kTHz
, kTHz
+
0
∆k, ..., kTHz + n∆k}, while the remaining parameters that govern Vm are considered
constant. Hence the term kFO ∆lFO is added as a constant phase to φ, yielding φ0 =
φ + kFO ∆lFO . In order to retrieve the value of A and φ0 , two different techniques
have been tested: 1) a fitting of the cosine function is performed retrieving the value
of amplitude and phase; and 2) a Fourier transform of the received signal is performed
and amplitude and phase of the maximum returned value are considered. Note that
96
Chapter 5
in both cases the sampling should fulfill Nyquist in order to avoid ambiguities in the
estimation, since no information a priori of kTHz is known.
In practice this method does not give good results due to the uncertainty in the thermal
tuning. The precision required in the tuning is on the order of few MHz, far beyond
the precision given by the laser temperature controller. In addition, the thermal tuning
is slow due to the inertia inherent to thermal systems.
3. As in the method described in the point 2, kTHz is swept but instead of using thermal
tuning, a laser current modulation is used. The frequency of one of the lasers can be
modulated by introducing a slight variation on its biasing current. This effect is directly
translated to kTHz . In particular, the modulation ratio of the lasers of the THz-CW
system is 1 GHz/mA. Figure 5.14 shows the effect of a current modulation ramp of
300µA in the measured voltage.
After a set of tests of the methods explained in points 2 and 3, the latter has been chosen
due to its precision and fast acquisition speed. This method yields a complex electric field
measurement each 0.5 s, and can be speeded up by reducing the period of the modulating
ramp. However, in our case the maximum speed is limited by the minimum integration time
of the lock-in amplifier and by the required noise level. A good tradeoff has been found setting the ramp period to 0.5 s and the time constant of the lock-in amplifier to 10 ms. Once
the whole voltage trace is acquired, the amplitude and phase of the signal is obtained by performing the Fourier transform of the data and selecting the point with maximum amplitude,
as described in the point 2.
It has to be pointed out that the synchronization between the function generator used to
create the current ramp and the ADC should be precise in order to maintain the repeatability
of the phase measurements throughout time. The synchronization has been achieved by using
a hardware trigger that creates a positive voltage edge at the beginning of each ramp starting
a new acquisition of the ADC.
5.3.3
Data calibration
The tomographic algorithm requires, for each reconstruction frequency, a system with two
rotation movements: the sample rotation with angle θ0 and the receiver PCS rotation with
angle θ. Both rotations share the rotation axis of the sample rotation servo. In the measurement process, the sample rotation angles have been set to θ0 = {0, 22.5, 45, ..., 337.5} deg,
yielding a number of 16 different sample angles. For each sample angle θ0 , 61 receiver angles are swept θ = {−30, −29, ..., 0, ..., 29, 30} deg. Considering the 9 different frequencies
acquired f = {100, 200, 300, 400, 500, 534, 600, 700, 800} GHz, the total number of acquisition is 9351 electric field points if the empty chamber and calibration points are considered.
Figure 5.15 shows the evolution of the phase of the system throughout time. A large phase
drift is observed in the time of a complete acquisition for a certain frequency (90 minutes).
The Fig. shows the necessity of phase calibration to reconstruct the measurement since the
phase drift of the system would mask the phase variation caused by the sample. In order
to calibrate the measurement, some calibration points should be taken. The following data
acquisition sequence describe the acquisition order of the calibration points and the empty
chamber:
Sample: 337.5º
Sample: 315º
Sample: 292.5º
Sample: 270º
Sample: 247.5º
Sample: 225º
Sample: 202.5º
Sample: 180º
Sample: 157.5º
Sample: 135º
Sample: 112.5º
Sample: 90º
Sample: 67.5º
Sample: 45º
Sample: 22.5º
Sample: 0º
97
Empty chamber
5.3 Measurements
0
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−1400
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10
20
30
Calibration point
40
50
t [min]
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70
80
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Figure 5.15: Calibration curve interpolated from the acquired calibration points. The measurement
intervals depending on the sample position are also shown.
1. Set the desired frequency by thermal tuning.
2. Wait 50 minutes until the inertia of the system is residual and the phase of the signal is
stable.
3. Translate the sample to a position where does not interfere in the electric field and
measure a calibration point at θ = 0 ◦ .
4. Measure the empty chamber by acquiring the 61 points of θ.
5. Measure a calibration point at θ = 0 ◦ .
6. Move the sample to the measurement position, set θ0 = 0 ◦ and perform the whole set
of measurements of θ.
7. Repeat actions 3 and 6, increasing the value of θ0 until θ0 = 337.5 ◦ .
8. Translate the sample to a position where does not interfere in the electric field and
measure the final calibration point at θ = 0 ◦ .
An schematic of the acquisition sequence is shown in Fig. 5.15 where the calibration
points and the time slots where the acquisition points for different θ0 are depicted. The phase
drift curve of the system can be obtained by interpolating the calibration points. Since the
acquisition time instant is stored for each electric field point, the phase can be compensated
point by point by normalizing the electric field by the phase at a certain time instant. Several tests without phase calibration have been performed without success. In those cases
98
Chapter 5
Purge controller
Purging
Glovebox
Nitrogen tank
Figure 5.16: Photograph of the Time-Domain spectroscopy system placed on an optical table. The
THz path is placed inside a hermetic sealed glovebox used to purge the environment to reduce the water
vapor.
the reconstruction of the scenario yields an image consisting in pure noise. However, if a
proper calibration is performed, the phase drift can be completely compensated with a residual phase noise estimated in 10 ◦ . The residual noise has a random behavior and can come
from the phase noise of the lasers or caused by instabilities in the thermal control. In any
case, this phase noise does not apparently distort the images as will be shown in Section 5.3.
5.3.4
Spectroscopic characterization
A pharmaceutical compound with commercial name Polaramine Repetabs has been chosen
as a pharmacological sample to perform the spectroscopic imaging measurements. The active
ingredient is Dexclorfeniramine Maleate, a histamine antagonist. The Polaramine has been
chosen as a sample due to two reasons: 1) it can be obtained without medical prescription;
and 2) it has a high content on α − lactose (main excipient). The molecular interaction of
the α − lactose with the electromagnetic waves has been already studied in [87] resulting in
a rotational mode at 0.525 THz, two translation modes at 0.993 THz and 1.110 THz, and a
rotational mode at 1.32 THz. Therefore the Polaramine is a good candidate for spectroscopic
imaging since it has absorption peaks distributed along the THz frequency band. Nevertheless, we will center out attention in the absorption produced at 525 GHz.
A THz-TDS system has been used to characterize the response of the pharmacological
compound in the THz band. Figure 5.16 shows a photograph of the measurement system
placed on an optical table. An hermetically sealed glovebox has been used to create an atmosphere with a controlled value of humidity. The air humidity in THz path should be as low
as possible to avoid the effect of the multiple water vapor absorption peaks in the spectrom-
5.3 Measurements
99
Laser Delay Stage
Polarizing
Beamsplitter
Receiver Beam
Transmitter Beam
Common Laser Beam
Femtosecond Laser @ 780 nm
Figure 5.17: Optical path of the Time-Domain system. The femtosecond laser, the delay sage and the
various optical components are shown in the image.
Photoconductive Receiver Antenna
Photoconductive Emitter Antenna
Collimating Lenses
Transimpedance
amplifier
Mirror
Focusing Lenses
Mirror
Figure 5.18: Terahertz path of the Time-Domain system. The image describes the main components of
the THz path.
100
Chapter 5
eter response. The control has been achieved by purging with nitrogen gas the water vapor
contained in the ambient air. Note that the purging system composed by a nitrogen tank and
a purge control unit are also shown in Fig. 5.16. Since only the THz path should be purged,
the transmitter and receiver optical paths are kept outside of the glovebox, introducing the
laser beams through the acrylic back panel.
The optical subsystem of the spectrometer is shown in Fig. 5.17. The femtosecond laser,
the optical delay stage and the multiple optical mirrors and accessories composing the subsystem are shown in the photograph. In addition, the path of both receiver and transmitter
laser beams are shown in blue and green respectively. At the right of the image, the beams
are aimed directly to the photoconductive antennas placed inside the glovebox. The antennas
are shown in Fig. 5.18 together with lenses in charge of collimating and focusing the THz
beam, two mirrors that rotate the beam 90 ◦ and a TIA. The Polaramine powder is placed
using a sample holder in between both focusing lenses in order to perform the measurement.
The technique used to measure the spectrum of the sample is the one usually used in a
THz-TDS:
• The THz pulse is sampled by using the optical delay stage. The linear step of the stage
∆x is translated to a temporal step in the sampled pulse of of ∆t = 2∆x/c, where c is
the speed of light.
• The voltage given by the TIA is processed by the lock-in amplifier and acquired using
a ADC. For each step of the linear stage a voltage value is acquired, resulting in a total
of Np points.
• Once the complete pulse is retrieved, a Discrete Fourier Transform (DFT) is performed
in order to obtain the frequency spectrum of the measurement.
The maximum frequency value and the frequency resolution are given by the properties
1
; and the frequency
of the DFT. Therefore, the maximum frequency value is: fmax = 2∆t
1
resolution is given by the maximum time span: ∆f = ∆tNp . Figure 5.19 shows the measured
spectrum of the system without sample with two different humidity levels: 30% and 2%. In
this measurement, ∆t = 0.125 ps whereas the number of points is Np = 200. The water
vapor absorption peaks appear in the curve corresponding to the measurement with 30% of
humidity. Note the drastic reduction of the peaks in the purged measurement. This Figure
shows that a purged measurement should be performed when the expected absorptions of the
sample are close to the water vapor absorptions, otherwise the measurement will be masked.
Figure 5.20 shows the measured absorption spectrum of a Polaramine sample. The measurement with the sample is normalized by the free-space measurement in order to eliminate
the response of the system from the measurement. Moreover, the linear response of the scattering produced in the sample has been retrieved by using a linear regression and subtracted
from the measurement. As expected, an absorption line appears at 525 GHz, confirming the
pharmaceutical as a good candidate for spectroscopic imaging.
It has to be pointed out that the response expected at the frequency of 0.993 THz is not
noticeable since it is masked by noise. Despite the dynamic range of the system at 1 THz
is close to 50 dB, the high scattering produced by the pharmaceutical powder attenuates the
signal around 45 dB at 1 THz. This problem can be overcome by using a press to compact
the powder.
5.3 Measurements
101
Normalized Amplitude [dB]
0
−20
−40
−60
−80
100
Ambient humidity: 30%
Purged humidity: 2%
500
1000
1500
2000 2500
f [GHz]
3000
3500
4000
Figure 5.19: Characterization of the signal spectrum produced by the THz-TDS system available in
the AntennaLab THz laboratory. The spectrum has been measured with two different humidity levels:
30 % and 2 %. The reduction in the level of the water vapor absorption peaks is clearly noticeable.
6
Absorbance [dB]
5
4
3
2
1
0
300
400
500
600
700
f [GHz]
800
900
1000
Figure 5.20: Absorption spectrum of the pharmacological compound with commercial denomination
Polaramine Repetabs.
5.3.5
Tomographic imaging
Several measurements of different scenarios have been performed to test the imaging capabilities of the reconstruction algorithm in the THz frequency range. The difference among
different scenarios resides in the type of sample and their disposition in the scene. The samples are based on a Rohacell structure as described Section 5.3.1 and may contain Polaramine
depending on the test.
Figure 5.21 shows the image reconstruction of a scenario consisting in a solid cylinder
of Rohacell material with 12 mm diameter displaced from the center of rotation. Since the
algorithm is based on a cylindrical geometry, it tends to easily reconstruct cylindric shapes
at the center of the image, even if the algorithm is not properly implemented in the computer. Therefore, a first test with a sample displaced from the center has been performed in
order to validate the implementation of the reconstruction algorithm. The cylinder is retrieved
Chapter 5
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102
0.6
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(i) 800 GHz
Figure 5.21: Reconstructed images from the measurements of a Rohacell cylinder of 12mm diameter
displaced from the center of rotation. Each image corresponds to a reconstruction of the contrast at a
single frequency: (a) 100 GHz, (b) 200 GHz, (c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz,
(h) 700 GHz, (i) 800 GHz.
properly from frequencies up to 600 GHz. In the following frequencies the SNR of the measurements decreases, being translated to the image as an increment of noise. In addition,
the shape of the cylinder tends to be concentrated to the center of the image. This is caused
by the narrowing of both the illumination and reception THz beams as the frequency is increased. At high frequencies the THz beams illuminate the sample partially, and therefore
the reconstruction shape does not perfectly match with the original sample.
Additional tests have been performed without including the pharmaceutical compound in
the sample. Figure 5.22 shows two reconstruction from different scenarios. In Fig. 5.22(a)
a solid Rohacell block with triangular shape, and displaced from the center has been reconstructed. The shape obtained from the measurement does not completely match with the
block shape. The main discrepancies occur at the edges that appear rounded instead of sharp.
The main cause is the lack of spatial resolution to properly retrieve the edges. Either a higher
frequency or a higher span of the reception angle θ should be used to improve the spatial
resolution, and hence increase the reconstruction quality of the edges. A Rohacell cylinder
of 12 mm diameter with an empty inner-cylinder of 6 mm diameter has been measured and
the resulting image is shown in Fig. 5.22(b). The center hole is reconstructed with the proper
dimensions, confirming the penetration capabilities of the THz radiation in the Rohacell material. Therefore, Rohacell is a proper material to be used as a sample holder to perform the
spectroscopic imaging.
The test on spectroscopic imaging has been performed using a centered Rohacell cylinder
with 12 mm diameter and inner-cylinder of 6 mm filled with Polaramine. Figure 5.23 shows
the reconstructed images of the sample. The cylinder is centered at the main rotation axis and
therefore it appears centered in the image. The dynamic range of the images is fixed and the
results have been normalized by the frequency response of the system, therefore the images
5.3 Measurements
20
20
Rohacell with
triangular shape
Rohacell with
center hole
10
y [mm]
10
y [mm]
103
0
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0
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400 GHz
−20
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−10
0
10
x [mm]
(a)
200 GHz
−20
20
−20
−10
0
10
x [mm]
20
(b)
Figure 5.22: (a) Reconstructed image of a Rohacell block with triangular shape; and (b) reconstructed
image of a Rohacell cylinder with a hole of 6 mm diameter.
can be compared among them. As in the images appearing in Fig. 5.21, as the frequency
increases the level of noise in the images increases as well and reconstruction quality of the
cylinder decreases. In general, only the outer shape of the cylinder is reconstructed and the
polaramine contrast is not perceived. However in the images of Fig. 5.23(c) and 5.23(h),
the contrast is slightly shown as a superposition of two circles. Note that the inner cylinder
is not properly centered in the main cylinder, but a slight shifted to the positive x-axis. The
main variation in the images appears in Fig. 5.23(f), where an attenuation in the zone of
the image where the Polaramine is placed. However the zone corresponding to the Rohacell
cylinder is still properly retrieved. It has to be pointed out that due to the slight shift in
the frequency calibration of the THz-CW system, the attenuation occurs around 534 GHz
instead of 525 GHz as measured with the THz-TDS system and presented in section 5.3.4.
This attenuation zone appearing at the frequency where the Polaramine has an absorption line
confirms the suitability of the algorithm to perform spectroscopic imaging since it is capable
of showing in the image the attenuation of the materials that compose the scene, depending
on the frequency.
In order to check the attenuation level produced in the zone, an integration of the retrieved
image contrast values in the zone where the Polaramine is placed has been performed. A
result of the integration depending on the frequency is shown in Fig. 5.24. A clear absorption
peak appears at 534 GHz, however the rest of the plot is not as flat as expected. This effect
can be produced by the fact that the scenario does not fulfill the Born condition, since the
relative permittivity of the Polaramine is around 2. The results obtained from the Polaramine
are compared with the ones obtained from the Rohacell sample shown in Fig. 5.21. The
result obtained from the Rohacell presents no significant absorption peaks since the Rohacell
does not have an spectral footprint in the studied frequency band. These results reveal that
the algorithm is useful when qualitative images are required, and no quantitative information
can be obtained since the main assumption of the reconstruction algorithm is not fulfilled.
Therefore, no information about concentration of the chemical substance can be obtained.
The algorithm is limited to detect and identify the pharmaceutical compound.
104
Chapter 5
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(h) 700 GHz
−10
0
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x [mm]
20
(i) 800 GHz
Figure 5.23: Reconstructed images from the measurements of a Rohacell cylinder of 12 mm diameter
filled with Polaramine powder covering a diameter of 6 mm. Each image corresponds to a reconstruction
of the contrast at a single frequency: (a) 200 GHz, (b) 300 GHz, (c) 400 GHz, (d) 500 GHz, (f)
534 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz.
Relative absorption [dB]
0
−1
−2
−3
−4
Polaramine
Rohacell
−5
−6
200
300
400
500
600
700
800
f [GHz]
Figure 5.24: The blue curve shows the result of the integration of the image zone where the Polaramine
is placed, depending on the frequency. The green curve shows the resulting integration of the zone where
the Rohacell is placed from the set of images shown in Fig. 5.21.
5.4
Conclusions
A THz tomographic reconstruction technique has been presented in this chapter. The algorithm required to focus the measured scattered field from the sample has been described,
and its suitability for imaging reconstruction at THz frequencies has been assessed. The
spectroscopic capabilities of the algorithm have been validated at THz frequencies with a
pharmaceutical compound having a molecular absorption resonance at 525 GHz.
5.4 Conclusions
105
A method to acquire complex electric field values with a THz-CW system has been developed. The method is based on modulating the laser current to shift the THz frequency
and has been proven to be appropriate to measure the complex field values required to reconstruct the image. Acquisition speeds below 1 s can be easily achieved by using this method.
However, a main drawback of the THz-CW has been found consisting of the large phase
drift throughout time. A calibration method consisting of acquiring several calibration points
and interpolating a phase calibration curve has been required to properly retrieve the images.
Each acquisition has been normalized by the phase drift value corresponding to its acquisition
time. This method have provided positive results on the image reconstruction since different
sample shapes and distributions have been tested and reconstructed successfully.
The spectroscopic capabilities of the algorithm have been validated by performing simulations and measurements. Only qualitative images can be obtained since the Born assumption
of the algorithm is not fulfilled in the imaged scenarios. Therefore, the images do not provide
information about concentration levels of the different materials and substances in the scene.
Nevertheless, the detection and identification capabilities of the algorithm have been assessed
yielding proper identification of the spectral footprint of the pharmaceutical compound under
test.
106
Chapter 5
Thesis Conclusions
C HAPTER 6
Conclusions and discussion
chapter describes the main contributions of this thesis in the areas of MillimeterWave (mmW) passive imaging and terahertz imaging. In addition, the CONSOLIDER
project objectives that have been fulfilled thanks to the work presented in this thesis are also
stated in the following lines. At the end of the chapter, the guidelines to continue with the
work performed in the thesis are given.
T
HIS
6.1
Conclusions
The work presented in this document is related with a research line that pursues two main
goals: 1) the development of a mmW camera for real-time acquisition of close-range images; and 2) the development of a terahertz imaging system for detection and identification
of chemical compounds.
The author has encountered several problems when addressing the proposed goals. This
has lead to a deep research on technology, techniques and methodology in the areas of mmW
and terahertz imaging with the aim of solving the mentioned issues. The following list details
the concluding remarks extracted in the pathway to the 94 GHz real-time camera development:
• The several tests performed with a single-receiver mechanically-scanned screener based
on a total-power radiometer have provided practical experience to the author, permitting to extract several conclusions:
1. Despite theoretically is feasible to obtain real-time (ts < 1) images with a singlereceiver screener with a proper radiometric resolution, the mechanical complexity
that presents the antenna aiming system makes this screener practically unfeasible.
2. In order to detect concealed objects in low-contrast scenarios, such as indoor environments, a radiometric resolution below 1 K is required. However, in outdoor
110
Chapter 6
scenarios the reflection of the sky strongly improves the contrast of the scenario,
reducing the performance requirements of the screener in terms of radiometric
resolution.
3. If the acquisition speed is not important performance parameter of the application,
a single-receiver screener is a good choice due to its simplicity and effectiveness.
• In order to decide which is the optimal radiometric geometry for close-range screening,
a performance study of three different radiometers (Two-Dimensional Synthetic Aperture (2D-SA), One-Dimensional Synthetic Aperture (1D-SA) and Real-Aperture (RA))
has been performed taking into account the distortion produced by placing the scenario in the near-field distance of the receiver array. The following conclusions can be
obtained from the results of the study:
1. When compared with the same front end parameters, spatial resolution and imaging rate, 2D-SA, 1D-SA and RA radiometric sensitivity is equivalent and not a
driver to select one of the options, however off-boresight radiometric resolution
degrades as a function of ξ 2 + η 2 in the synthesized cases.
2. The optimum performance is achieved when imaging at a fixed range and the
Half-Power Beamwidth (HPBW) of each single antenna in the array matches the
scene field of view. This condition is always feasible, in a first approach, independently of the imaging geometry and requirements.
3. Due to the small array size, mmW operation also allows for very large predetection bandwidths and close range configurations to improve radiometric sensitivity
while minimizing decorrelation effects and Noise Figure (NFI) distortion.
4. An sparse 1D-SA radiometer can be used with a moving walkway to perform
personnel screening avoiding mechanical movements with an optimum number
of mmW receivers.
• From the latter conclusion presented in the previous point it can be extracted that the
one-dimensional sparse interferometric radiometer achieves a good tradeoff between
radiometric performance and number of receivers for close-range screening purposes.
However, the acquisition of multiple correlations of large bandwidth signals required
to retrieve the visibilities of the scene represents a major drawback in this radiometer.
Hence, a method to overcome the problem of routing and correlating all the antenna
signal pairs in an interferometric radiometer by upconverting the Radiofrequency (RF)
signal to the optical domain has been developed in this thesis, yielding the following
conclusions:
1. A distribution and correlation of the mmW signals in the optical domain can
strongly simplify the processing of the multiple correlations required in a interferometric radiometer.
2. The method has been tested by performing measurements of several scenarios,
confirming the suitability of the method.
3. The receiver temperature of the system is not critically degraded by converting
the signal to the optical domain since the LNA placed at the front-end fixes the
noise figure for the whole receiver chain.
6.2 Future Research
111
4. For systems with high number of receivers a Single-Sideband (SSB) modulation
should be used in order to achieve real-time imaging with bandwidths in the order
of the GHz.
In the research of a THz tomographic imaging system for chemical compound detection
and identification, a reconstruction algorithm based on a Born approximation has been used.
The following conclusions are extracted from the work performed in this topic:
1. The cylindrical diffraction tomography algorithm shows the capability of retrieving
spectral information of the objects appearing in the reconstructed image.
2. Even though the Terahertz Continuous Wave (THz-CW) system does not provide direct
complex signal information, amplitude and phase of the signal can be retrieved by
sweeping the THz signal by modulating the laser current with a ramp.
3. The images cannot be reconstructed if the phase drift along time of the system is not
calibrated.
4. Only qualitative results can be obtained from the images, since the Born approximation
is not valid for the studied cases.
6.2
Future Research
The following lines describe the work that can be performed as a continuation of the research
presented in this thesis:
1. Develop the optical distribution part of the optical correlation system in order to validate the suitability of the method with multiple receivers.
2. Build an industrial prototype of a close-range screener based on a linear interferometric
radiometer with the optical cros-correlator method developed in this thesis.
3. Test the tomographic algorithm by measuring samples containing multiple chemical
compounds to ensure the suitability of the method.
4. Design tomographic cylindrical array in order to perform THz spectroscopic imaging
in real-time using the algorithm described in this document.
112
Chapter
A PPENDIX A
Close-Range Millimeter-Wave Passive Images
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Several images have been acquired using the Total-Power Radiometer (TPR) described in
chapter 2. This appendix includes some of these radiometric images taken from the PhD
students of the AntennaLab group of the Signal Theory and Communications Department
(TSC) department. The images have been acquired in an outdoor environment with a metallic
rear panel that reflects the sky temperature towards the radiometer. This improves the contrast
of the person with respect the background. The approximate spatial resolution is around 3 cm
in each axis whereas the radiometric sensitivity of the image is around 2 K.
The images have been taken in different measurement trials and the format does not match
among all of them. Figure A.1 shows images with 60x100 cm2 dimensions. In those images
the body can be seen from the neck to the knees. The upper part of the body reflects the
temperature of the sky and is seen as a cold surface whereas the bottom part is seen as a hot
surface since reflects the heat from the floor. Figure A.2 presents images with 50x70 cm2
dimensions. In this case only the center body is seen with exception of Fig. A.2(b) where the
entire head is shown.
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Figure A.1: Outdoor images with 60x100 cm2 dimensions.
Appendix A
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Figure A.2: Outdoor images with 50x70 cm2 dimensions.
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Acronyms
16QAM
16-state Quadrature Amplitude Modulation
1D-SA
One-Dimensional Synthetic Aperture
2D-SA
Two-Dimensional Synthetic Aperture
ADC
Analog to Digital Converter
ADC
Analog-to-Digital Converter
ALMA
Atacama Large Millimeter/Submillimeter Array
ASK
Amplitude Shift Keying
CMOS
Complementary Metal-Oxide Semiconductor
CMOS
Complementary Metal-Oxide-Semiconductor
CT
Computed Tomography
CW
Continuous Wave
DC
Direct-Current
DFB
Distributed Feedback
DFT
Discrete Fourier Transform
DSB
Double-Sideband
EFoV
Effective Field of View
FEM
Finite Element Method
FF
Far Field
FFT
Fast Fourier Transform
FMCW
Frequency-Modulated Continuous-Wave
116
Acronyms
FoV
Field of View
FPGA
Field Programmable Gate Array
FT
Fourier Transform
HDTV
High Definition Television
HPBW
Half-Power Beamwidth
iFFT
inverse Fast Fourier Transform
IF
Intermediate Frequency
IFoV
Instantaneous Field of View
iFT
inverse Fourier Transform
JPL
Jet Propulsion Laboratory
LNA
Low-Noise Amplifier
LO
Local Oscillator
MIRAS
Microwave Imaging Radiometer using Aperture Synthesis
MMIC
Monolithic Microwave Integrated Circuit
mmW
Millimeter-Wave
MoM
Method of Moments
NASA
National Aeronautics and Space Administration
NFI
Noise Figure
NF
Near Field
NTT
Nippon Telegraph and Telephone Corporation
PCA
Photoconductive Antenna
PCS
Photoconductive Switch
PID
Proportional-Integral-Derivative
PLO
Phase-Locked Oscillator
PML
Perfect Matched Layer
PO
Physical Optics
PVC
Polyvinyl Chloride
QCL
Quantum Cascaded Laser
Acronyms
117
RA
Real-Aperture
RF
Radiofrequency
RMS
Root-Mean-Square
SA
Synthetic Aperture
SMOS
Soil Moisture and Ocean Salinity
SNR
Signal to Noise Ratio
SSB
Single-Sideband
THz-CW
Terahertz Continuous Wave
THz-TDS
Terahertz Time-Domain Spectroscopy
TIA
Transimpedance Amplifier
TPR
Total-Power Radiometer
TSC
Signal Theory and Communications Department
UPC
Polytechnic University of Catalonia
USB
Universal Serial Bus
UTC-PD
Uni-travelling Carrier Photodiode
VNA
Vectorial Network Analyzer
WLAN
Wireless Local Area Network
WPAN
Wireless Personal Area Network
118
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Author Publications and Patents
Journal articles
[J1] Nova, E., J. Romeu, S. Capdevila, F. Torres, and L. Jofre, “Optical Signal Processor for Millimeter Wave Interferometric Radiometry,” Geoscience and Remote Sensing, IEEE Transactions on,
vol. In press.
[J2] Nova, E., J. Romeu, F. Torres, M. Pablos, J. Riera, A. Broquetas, and L. Jofre, “Radiometric
and Spatial Resolution Constraints in Millimeter-Wave Close-Range Passive Screener Systems,”
Geoscience and Remote Sensing, IEEE Transactions on, vol. 51, no. 4, pp. 2327–2336, 2013.
Conference articles
[C1] Nova, E., G. Roqueta, J. Romeu, and L. Jofre, “Characterization of Pharmaceuticals using Terahertz Time Domain Spectral-Tomography,” in Antennas and Propagation (EUCAP), 2013 7th
European Conference on, 2013.
[C2] Nova, E., D. Rodrigo, J. Romeu, and L. Jofre, “94 GHz cassegrain reflector antenna performance
characterization,” in Antennas and Propagation (EUCAP), 2012 6th European Conference on,
march 2012, pp. 3442 –3445.
[C3] Nova, E., J. Romeu, F. Torres, A. Broquetas, and L. Jofre, “Optical Cross-Correlation of Millimeter Wave Signals Applied to Interferometric Radiometry,” in Infrared, Millimeter and Terahertz
Waves (IRMMW-THz), 2012 37th International Conference on, 2012.
[C4] Nova, E., J. Romeu, A. Broquetas, F. Torres, and L. Jofre, “Optical Cross-Correlation of Wband Radiometric Signals,” in XXVII Simposium Nacional de la Unión Cientı́fca Internacional de
Radio (URSI 2012), 2012.
[C5] M. Alonso, C. Guerra, Nova, E., J. Abril, J. Romeu, N. Llombart, and L. Jofre, “100 GHz retina
for THz tomographic imaging,” in Infrared, Millimeter and Terahertz Waves (IRMMW-THz), 2011
36th International Conference on, oct. 2011, pp. 1 –2.
[C6] Nova, E., J. Abril, J. Romeu, A. Broquetas, F. Torres, and L. Jofre, “Characterization of a 94
GHz radiometric imager with mechanical beam-scanning,” in Microwave Workshop Series on
Millimeter Wave Integration Technologies (IMWS), 2011 IEEE MTT-S International, sept. 2011,
pp. 164 –167.
[C7] J. Abril, Nova, E., A. Broquetas, A. Aguasca, J. Romeu, and L. Jofre, “Deforming and relief
interferometric sar imaging at W-band,” in Infrared, Millimeter and Terahertz Waves (IRMMWTHz), 2011 36th International Conference on, oct. 2011, pp. 1 –2.
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Bibliography
[C8] Nova, E., J. Abril, J. Romeu, A. Broquetas, F. Torres, and L. Jofre, “Imaging performance of a
94 GHz radiometer,” in XXVI Simposium Nacional de la Unión Cientı́fca Internacional de Radio
(URSI 2011), 2011.
[C9] J. Abril, Nova, E., A. Broquetas, A. Aguasca, J. Romeu, and L. Jofre, “Micrometric Deformation
Imaging Assessement for W-band FMCW Radar,” in XXVI Simposium Nacional de la Unión
Cientı́fca Internacional de Radio (URSI 2011), 2011.
[C10] J. Abril, Nova, E., A. Broquetas, A. Aguasca, J. Romeu, and L. Jofre, “Micrometric deformation
imaging at W-band,” in Microwave Workshop Series on Millimeter Wave Integration Technologies
(IMWS), 2011 IEEE MTT-S International, 2011.
[C11] L. Jofre, J. Romeu, S. Capdevila, J. Abril, Nova, E., and M. Alonso, “The challenging world of
Terahertz radiation and imaging,” in Antennas and Propagation (EUCAP), Proceedings of the 5th
European Conference on, april 2011, pp. 3470 –3475.
[C12] Nova, E., J. Abril, J. Romeu, A. Broquetas, F. Torres, and L. Jofre, “W-band radiometric imager
with mechanical beam-scanning,” in Infrared, Millimeter and Terahertz Waves (IRMMW-THz),
2011 36th International Conference on, oct. 2011, pp. 1 –2.
[C13] Nova, E., J. Abril, A. Broquetas, F. Torres, J. Romeu, and L. Jofre, “94 GHz short-range passive
imaging systems,” in XXV Simposium Nacional de la Unión Cientı́fca Internacional de Radio
(URSI 2010), 2010.
[C14] J. Abril, Nova, E., S. Capdevila, A. Broquetas, F. Torres, and L. Jofre, “Active and passive THz
systems for short-range imaging applications,” in Proc. Fourth European Conf. Antennas and
Propagation (EuCAP), 2010, pp. 1–4.
[C15] J. Abril, Nova, E., A. Broquetas, J. Romeu, L. Jofre, G. Pérez, J. A. Encinar, M. Barba,
D. Sánchez, and M. Ferrando, “Active Short-Range Imaging Systems Working at 94 GHz,” in
XXV Simposium Nacional de la Unión Cientı́fca Internacional de Radio (URSI 2010), 2010.
[C16] J. Abril, Nova, E., A. Broquetas, F. Torres, J. Romeu, and L. Jofre, “Combined passive and
active millimeter-wave imaging system for concealed objects detection,” in Proc. 35th Int Infrared
Millimeter and Terahertz Waves (IRMMW-THz) Conf, 2010, pp. 1–2.
[C17] F. Torres, J. Abril, Nova, E., A. Broquetas, and L. Jofre, “Far field condition in passive interferometry for security screening applications,” in Proc. Fourth European Conf. Antennas and
Propagation (EuCAP), 2010, pp. 1–4.
[C18] J. Abril, Nova, E., A. Broquetas, A. Aguasca, J. Romeu, B. Jofre, L. Mencı́a, J. Grajal, J. P.
Pascual, T. Fernández, and A. Tazón, “mmW FM-CW Ground-based SAR,” in XXV Simposium
Nacional de la Unión Cientı́fca Internacional de Radio (URSI 2010), 2010.
[C19] Nova, E., J. Abril, A. Broquetas, J. Romeu, and L. Jofre, “Terahertz Spectroscopic Material
Characterization and Imaging,” in XXV Simposium Nacional de la Unión Cientı́fca Internacional
de Radio (URSI 2010), 2010.
[C20] Nova, E., J. Abril, M. Guardiola, S. Capdevila, A. Broquetas, J. Romeu, and L. Jofre, “Terahertz subsurface imaging system,” in Proc. Fourth European Conf. Antennas and Propagation
(EuCAP), 2010, pp. 1–5.
[C21] Nova, E., J. Abril, M. Guardiola, S. Capdevila, A. Broquetas, J. Romeu, and L. Jofre, “Terahertz tomographic imaging technologies,” in XXIV Simposium Nacional de la Unión Cientı́fca
Internacional de Radio (URSI 2009), 2009.
Author Publications and Patents
127
Patents
[P1] Nova, E. and J. Romeu, “Correlador para múltiples receptores de señal de radiofrecuencia implementado con tecnologı́a óptica,” Spanish application Patent P201 231 599, 2012.
[P2] J. Encinar, G. Pérez, M. Barba, X. Quintana, M. Geday, J. Otón, A. Broquetas, J. Abril, and Nova,
E., “Antena reflectarray de haz reconfigurable basada en celdas multi-capa de cristal lı́quido,”
International application Patent PCT/ES2011/000 350, 2010.